STRENGTH FROM THE MARGINS

Restaging European Anthropologies

Andrés Barrera-González, Monica Heintz and Anna Horolets

I n what ways did Europeans interact with the diversity of people they encountered on other continents in the context of colonial expansion, and with the peasant or ethnic 'Other' at home? How did anthropologists and ethnologists make sense of the diversity of people and societies during the nineteenth and twentieth centuries, when the discipline was progressively being established in academia? This volume aims to sketch an intellectual and institutional portrait of a discipline that was originally oriented towards the study of the 'Other', by assessing the diversity of European intellectual histories within sociocultural anthropology. It aims to give more visibility to the 'smaller' European traditions of scholarly endeavour in the differentiated fields of sociocultural anthropology and ethnology, between which dialogue has sometimes been difficult due to each field's lack of awareness of the other's background of intellectual and academic engagement. It suggests that anthropology could find renewed strength by interrogating these 'anthropologies from the margins', which have distinct intellectual genealogies and histories and whose approaches to the study of culture are more sensitive to history, for instance, or to other related disciplines.

The term 'anthropology' in this volume is used as shorthand for both sociocultural anthropology and for what is labelled ethnology, ethnography or folklore studies, in particular national traditions and specific historical and academic contexts. It was only through considering these two fields together that we were able to engage a dialogue, on an equal footing, between distinct national traditions. 1 We chose to address the contours of 'Europeanness' in order to contribute to the dialogue that had already begun around the harmonization of higher education in Europe in the framework of the Bologna Process. It is customary in this context to speak about the goal of achieving a competitive 'European science'. However, we insist on the necessary plurality of these traditions and nowhere in this volume is the aim to produce one single 'European anthropology' in the future mentioned. Through a description of past developments, we suggest that if European anthropologies are in any way scientifically 'competitive', it is because of their mutual breeding and cross-fertilization and not because of their homogenization. Thus, alongside their inspection of the past lineages and entanglements of diverse scholarly traditions and schools, the authors in this volume contemplate the present-day situation of European anthropologies and ethnologies. They reveal the new challenges facing the discipline in the context of the harmonization of European higher education and of the increased liberalization of the management of universities. They point out the difficulties encountered by a discipline known for its reflexivity, in making its results available for what could sometimes be uncritical public use.

In order to follow the rationale of the volume, this introductory chapter is organized in two parts. In the first part we will consider the diversity of anthropology's traditions in Europe through their association with the project of societal modernization, which took different forms at its early stages depending on whether anthropology accompanied the unfolding of a national identity or the discovery of the richness of an empire. In the second part we will look towards the future, and caution against the ongoing existence of inequalities in the production and diffusion of anthropological knowledge, and against the too rigid new European standards in teaching and research. Imposed by a similar project of societal modernization, these standards lead to new forms of power differentiation in the academy and the impulse to build a global science could paradoxically result in new academic inequalities.

REMEMBERING THE PAST

In a notable book on the history of anthropology, George Stocking Jr makes a useful distinction (even if he somewhat simplifies the complexity of particular cases) between nation-building and empire-building anthropologies (Stocking 1984). This is a categorization of the discipline that is based on its socio-historical mode of implementation, which reflects, in turn, on the relation between the anthropologist and the Other. These two distinct ways of doing anthropology appear to share a common goal: the understanding and modernization of society. Focusing on the common goal of societal modernization contributes to reducing the perceived differences between ethnology (Volkskunde, the study of 'the people', of one's own national traditions) and sociocultural anthropology (Völkerkunde, the study of 'other peoples', particularly non-European peoples). This approach will equally allow us to emphasize the current challenges and dangers of building European anthropology in response to the imperative of social usefulness.

Rescuing 'Small' Traditions

One of the first questions to emerge in the process of writing an inclusive 2 social history of the discipline is: on what remarkable facts and events should it be constructed? This is followed by a consideration of who chooses, and when, what is deemed to be meaningful for its development.

The received wisdom is that anthropology was established in the academy at some point during the second half of the nineteenth century, through initiatives taken and institutions set up either in the United States [START_REF] Hinsley | Savages and Scientists] The Smithsonian and the American Indian: Making a Moral Anthropology in Victorian America[END_REF][START_REF] Hinsley | Savages and Scientists] The Smithsonian and the American Indian: Making a Moral Anthropology in Victorian America[END_REF]; [START_REF] Bieder | Science Encounters the Indian, 1820-1880: The Early Years of American Ethnology[END_REF] or in Victorian Britain (Stocking 1984(Stocking , 1991;;[START_REF] Kuklick | The Savage Within: The Social History of British Anthropology, 1885-1945[END_REF][START_REF] Kuklick | The Savage Within: The Social History of British Anthropology, 1885-1945[END_REF]Kuklick ], 2008)). However, in a well-documented and thoroughly researched book, Han F. [START_REF] Vermeulen | Early History of Ethnography and Ethnology in the German Enlightenment[END_REF]Vermeulen ( , 2015) ) takes the beginnings of the discipline (under the names of Ethnographie and Ethnologie) back to the eighteenth century. It was in the context of the German Enlightenment, and in relation to extensive ethnographic work carried out by German scholars participating in Russian expeditions to Siberia, that these disciplines were established and received a decisive impulse in their practice and theory. 3 We can, of course, take the history back further, to antiquity, as some history of anthropology textbooks do, pointing out the relevance for anthropos-logos of works such as Herodotus' The History. 4 Accounts of prodigious journeys of travel and trade may also be considered precedents for anthropology. In this regard, there are certainly many authors and works that could be recalled as part of anthropology's intellectual lineage and heritage (see, for example, [START_REF] Hodgen | Early Anthropology in the Sixteenth and Seventeenth Centuries[END_REF]. In this volume, the chapter by Wolf-Knuts and Hakamies mentions such a relevant precedent in Finland and describes a case of discontinuity and overlooked 'ethnographic occasion' (a term forged by [START_REF] Pels | What Has Anthropology Learned from the Anthropology of Colonialism?[END_REF]Salemink, 2002 [1999]). The beginnings of Finnish folklore collection, including institutional efforts to 'preserve memories from bygone times', date back to as early as the sixteenth and seventeenth centuries. But due to geopolitical circumstances, as well as to cultural influences, it was not until much later that studying Finnish culture became a recognized discipline.

In this volume we have explicitly aimed to rescue these forgotten opportunities, which have indirectly shaped the discipline of anthropology but of which its practitioners today are not necessarily aware. This rewriting of the history of the discipline in Europe demanded an integration of ethnology and anthropology as two facets of the same pursuit. But also, through the presentation of 'big' or 'great' traditions, such as those of Germany or France, alongside 'small' or 'little' traditions, such as Croatia's or Finland's, we aimed to draw readers' attention to overlooked similarities and differences between variously situated and grounded European anthropologies. For the sake of clarity, in what follows we will use Stocking's categorization of empire-building and nation-building anthropologies, while at the same time pointing out the historical elements that run beyond this categorization.

The Ideal of Societal Modernization in the Anthropologies Associated with Imperial and Neocolonial Governance

It has been sufficiently demonstrated that anthropology is inextricably associated with colonial and imperial endeavours (Asad 1973). This historical context relates to the commonplace assumption that anthropological inquiry arises from the (peaceful or violent) encounter with the Other: the distant and far apart Other, be it in time, space, culture and/or social organization.

In this sense, anthropology would be understood as stemming, in practice, from intellectual and moral reflection, not on a generic human being, but on human beings other than us. At the different historical junctures these would be the barbarians, pagans, savages or primitives situated beyond the political and civilizational boundaries of the colonial metropolis, or alternatively the rural folk, peasants, ethnic minorities and outcasts at home. It should be remembered that anthropology has made substantial progress in the academic establishment, primarily and mostly where and when it has demonstrated its usefulness for incorporating these 'Others' into the dominant national or colonial civility: as a tool of empire in colonial or neocolonial contexts, or as part of nation-building and/or statecraft pursuits. British social anthropology at the turn of the century (from the nineteenth to the twentieth century) is a case in point, considering its close association with the politics and policies of 'indirect rule', and in more general terms with the governing of the colonies [START_REF] Kuper | Anthropology and Anthropologists: The Modern British School, 3rd revised and enlarged edition[END_REF][START_REF] Kuper | Anthropology and Anthropologists: The Modern British School, 3rd revised and enlarged edition[END_REF]; L'Estoile, Neiburg and Sigaud 2005). In North America the establishment of the Bureau of American Ethnology in 1879 was also part and parcel of the conquest, 'pacification' and colonization of the Western frontier, and a useful means for the better government and administration of 'Indian affairs' in particular [START_REF] Hinsley | Savages and Scientists] The Smithsonian and the American Indian: Making a Moral Anthropology in Victorian America[END_REF][START_REF] Hinsley | Savages and Scientists] The Smithsonian and the American Indian: Making a Moral Anthropology in Victorian America[END_REF]; [START_REF] Mark | A Stranger in Her Native Land: Alice Fletcher and the American Indians[END_REF].

Looking back at the beginnings of academic anthropology, the project of societal modernization appears to have fuelled the development of anthropology as a discipline. This is epitomized in the role played by scientific and anthropological expeditions in the establishment of a science of anthropology. The ideals of the Enlightenment promoted the incorporation of academic-scientific goals into expeditions of geographic and strategic military exploration undertaken in the fifteenth and sixteenth centuries, which were sponsored and carried out by countries with colonizing ambitions and interests. Scientific expeditions in the eighteenth century had a predominantly geographical and naturalist character. However, the range of interests gradually widened to account not only for the geography, flora and fauna of the explored lands, but also their diverse peoples and cultures, adding to the naturalist scientific endeavour the resources of disciplines such as ethnography and ethnology. Throughout the nineteenth century there was continuity in this tradition of great exploratory undertakings, with an increase in the number of expeditions bearing strictly scientific-academic contents. As pointed out above, these endeavours were promoted and carried out by countries with substantial colonial possessions (the United Kingdom and France, for example; or countries like the United States and Russia, which had embarked on vast processes of expansion of their metropolitan frontiers towards the west and east respectively.

Among the expeditions guided exclusively or predominantly by anthropological concerns and carried out between the end of the nineteenth century and the middle of the twentieth century, there are some whose direct and decisive impact on the consolidation and expansion of academic anthropology is widely acknowledged. This is certainly the case of Cambridge University's 1898 anthropological expedition to the Torres Strait, led by Alfred Haddon [START_REF] Hart | The Place of the 1898 Cambridge Anthropological Expedition to the Torres Straits (CAETS) in the History of British Social Anthropology[END_REF]Herle and Rouse 1998) and the North Pacific expeditions (1897)(1898)(1899)(1900)(1901)(1902) under Franz Boas' intellectual aegis (Krupnik and Fitzhugh 2001). But there are other 'ethnographic occasions', which, if reconsidered, would illustrate the diversity of academic lineages and intellectual genealogies that converge in the history of anthropology. One of these is the significant case of Russian ethnographies, ethnologies and more canonical past and present sociocultural anthropologies, described by Sergey Sokolovskiy in this volume. Russia's tradition in the practice of the anthropological and ethnological sciences is characterized by sharp discontinuities and ruptures, and by the radical interference of state-government agendas and political ideologies. There was a very promising start back in the eighteenth and nineteenth centuries, when the country opened up to Western influence. The direct involvement of German scholars from the Enlightenment period in the researching and writing of the ethnography of Siberian peoples and cultures motivated local scholars to get involved in the task themselves [START_REF] Vermeulen | Early History of Ethnography and Ethnology in the German Enlightenment[END_REF](Vermeulen , 2015)). In the context of the great expansion of Russia's frontiers towards the east, the exploratory endeavours of people like Captain Vladimir Arsenyev, 5 carried out in the far eastern confines of the Russian Empire at the end of the nineteenth century, also set a very promising precedent, but this unfortunately did not have continuity or consolidate into a national tradition of ethnologyanthropology, as happened in similar circumstances in the United States. The opportunities opened up for U.S. anthropology by the joint North Pacific expeditions (1897)(1898)(1899)(1900)(1901)(1902) were lost to Russia due to political developments in the first decades of the twentieth century (revolutionary uprisings and tsarist autocratic setbacks; a devastating civil war; the triumph of the Bolshevik revolution and the consolidation of the Soviet regime). The above-mentioned radical political and ideological interferences, and the discontinuities that took place in Russia's history during the twentieth century, have had a very negative effect as regards the consolidation of an academic tradition in ethnology/anthropology in Russia 6 (Sokolovskiy in this volume).

… and the Resulting Vulnerability of the Discipline

When imperial projects were disrupted, the discipline was weakened. Here Russia is a case in point, but it is not the only one. One of the most striking examples of the history of anthropology's response to historical events is that of German and German-language anthropologies discussed by John Eidson in this volume, which went through a twentieth century marked by ruptures, to arrive at today's vigorous internationalizing impulse. One need only recall the disrepute the Volkskunde was brought into by its involvement with racialist and eugenic policies and the political and ideological agenda of National Socialism. The thorough critique of this school's legacy carried out by Hermann Bausinger, and the reformulation of its central purpose as an 'empirical science of culture', was an adequate point of departure for its renovation into the future [START_REF] Bausinger | Volkskunde, ou l'ethnologie allemande[END_REF][START_REF] Bausinger | Volkskunde, ou l'ethnologie allemande[END_REF]). But, during this time, new powerful actors had come onto the scene, forcing German-speaking anthropology to yield to the dominance of Anglo-Saxon anthropologies. Today, change in the German anthropological-ethnological landscape is in full swing, and the discipline is overcoming a highly controversial past, including with regard to Völkerkunde -the imperial and colonial kind of German anthropology [START_REF] Barth | One Discipline, Four Ways: British, German, French, and American Anthropology[END_REF]) -and reinventing its future.

If John Eidson's overview chapter on German-speaking anthropologies draws our attention to the dynamic character of processes of empires rising and empires crumbling, the chapters by Pier Paolo Viazzo on Italy and by Susana de Matos Viegas and João de Pina-Cabral on Portugal equally show the sensitivity of the discipline to historical evolutions, though in a less dramatic way. Portugal treasures a short but very fertile history in the practice of the anthropological and ethnological sciences: nation-building anthropologies inward oriented, and colonial or neocolonial anthropologies outward oriented (Ferraz de Matos 2013). There is a rich and diversified tradition of anthropology at home, as well as many substantial contributions by foreign social and cultural anthropologists from England, France and the United States. To these could be added the more recent contributions by social anthropologists from the former colony of Brazil (an example of what may be labelled 'reciprocal anthropology') and by a few Spanish anthropologists who are developing their fieldwork and professional careers in Portugal. But the deep and prolonged economic crisis threatens to undo the remarkable accomplishments of Portugal's sociocultural anthropology over the last few decades, as it forces a number of prominent anthropologists to migrate in order to make a new start or advance in their professional careers.

With regard to Italy, the schools of ethnology and sociocultural anthropology have incorporated a broad range of traditions and practices, some of them going back to the nineteenth century: intellectual traditions associated with nation-building processes, home and foreign contributions to the anthropology of Italy, and some colonial or neocolonial veins. Italy has the particularity of being one of the countries favoured by Europeanist and Mediterraneanist U.S. and British anthropologists. This is both a positive and a negative trait, as sometimes foreign anthropologists have 'either ignored local anthropological traditions or dismissed them as mere folklore studies' (Viazzo, in this volume). But locally, government interference, with incongruent and sometimes contradictory policy measures, reforms and counter-reforms, does not provide an environment where this rich blending of traditions can bear fully grown fruit (Viazzo, in this volume).

France represents a sort of 'third way' among the schools of anthropology that stem from an empire, as the development of French anthropology has been touched less by the disintegration of the French empire and more by the recent globalization trend that has pushed Anglo-Saxon anthropologies forward. One can observe that France (and in this regard also the other Francophone countries in Europe: Belgium and Switzerland) is where the differing traditions of ethnology, social anthropology and folkloristics (bearing the local denomination arts et traditions populaires) have taken more time to find a common ground for collaboration, or at any rate for intercommunication and cohabitation at the institutional and intellectual level. Moreover, the history of academic sociocultural anthropology (in the terms outlined at the beginning of this introduction) features many renowned French scholars who have become widely reputed ancestors and intellectual beacons for the discipline, in more than their fair share measured in purely demographic terms.

Empire-building anthropologies are as diverse as the empires they were helping to govern: 7 empires reaching out to territories far beyond the metropolis (e.g., Italy) and those ruling over adjacent territories (e.g., Russia). The chapters devoted to French, Italian, German, Portuguese and Russian traditions of sociocultural anthropology and ethnology are illustrative of this. They demonstrate how the production of anthropological knowledge contributed to and was fuelled by imperial ambitions; the impulses that have arisen from the need to tame these ambitions; and the consequences that ensued for the discipline when they failed.

Societal Modernization and the Anthropologies Associated with Nation-Building and Statecraft Pursuits

Asserting that the emergence of 'national' traditions of ethnology and sociocultural anthropology in countries like Poland or Finland was part of nation-and state-building projects sounds like a tautology. Yet, this tautology is worth articulating, since both nation-building and national traditions of the disciplines can be unfolded in a number of directions. Paying attention at this stage to the existing associations between nation-building and the disciplines of anthropology and ethnology is meaningful because of the emergence or reinstatement of new countries and independent states in Europe and also because of the constant development and renovation of these disciplines.

The most significant intellectual (and aesthetical) impulse for this type of engagement comes from the ideals of Romanticism and its concern with the common people and popular national cultures, notably from authors such as Johann G. Herder (1744-1803). Paradoxically, Herder's works, which have been widely influential in continental schools of ethnology, and the Volkskunde in particular, date from the peak years of the German Enlightenment, rather than from the Romantic period sensu strictu. Herder was very influential in the formation of folklore studies in Germany, and also in Scandinavia and Central and Eastern Europe [START_REF] Bausinger | Volkskunde, ou l'ethnologie allemande[END_REF](Bausinger [1971]: 26-39;]: 26-39;[START_REF] Bendix | Search of Authenticity: The Formation of Folklore Studies[END_REF]Vermeulen 2008: 226-28; and Wolf-Knuts and Hakamies; Bitušíková; Čapo and Zrnić; Ciubrinskas; and Eidson's chapters in this volume). An independent source of intellectual inspiration for the study of folklore, and a distinctive tradition in practice, stems from Greece's laografia (see Aliki Angelidou's chapter in this volume). Moreover, the Greek school of laografia has influenced ethnological practices in other countries in the Balkan region, for instance in Bulgaria.

One way or another, most, if not all, the anthropological schools and traditions in Europe (with the exception of the already mentioned case of British social anthropology) are or have at some point been associated with nation-building pursuits and their ideological justification, as well as with the substantiation of the respective nation's cultural and historical foundation. For instance, Finland's schools and traditions in doing anthropology-ethnology appear during the struggle for independence from its powerful neighbours Sweden and Russia. The Finish people and their national institutions found a key ally in this struggle in scholars of ethnology and folkloristics, who, armed with innovative methods, made substantial scientific and empirical contributions. Finland's tradition in the ethnological sciences is highly original and rich, for instance in its associations with linguistics and ethnolinguistics, history and oral history, literary criticism and mythology (see Wolf-Knuts and Hakamies in this volume).

A special case is that of the new anthropologies that are emerging or re-emerging in countries that have become independent since the fall of communist regimes in Eastern Europe and beyond, namely following the dissolution of Yugoslavia, Czechoslovakia and the Soviet Union. As the discipline is rapidly changing in these areas, it is interesting to continue to monitor the establishment or re-establishment of specific schools and traditions and watch whether 'the nation' and national-state pursuits remain their catalyser. Substantial work on this topic has been carried out in the last twenty years by scholars such as Peter Skalník (Skalník 2000(Skalník , 2002(Skalník , 2004)), Chris Hann (Hann, Sárkány and Skalník 2005;Boškovic and Hann 2013), and others (Mihailescu, Iliev and Naumovic 2008;Boškovic 2008;Kürti and Skalník 2009). Chapters on Croatia, Slovakia and Lithuania in this volume converge on the importance given to the building or recovery of national identity in the recent development of ethnology and social anthropology in these countries.

The nation-state can be seen as a vehicle for modernization or, rather, it is the need to step up modernization processes that favoured the flourishing of nation-states. As part of this driving force, ethnology was concerned with studying the soul of the nation: its customs, culture, values and identity. The modernization process is also understood as a particular kind of rationalization: the emergence of new modes of knowledge and its secularization, a distancing from religion, and the concomitant development of new modes of production and ownership. Modernization met with criticism (e.g., from the standpoint of Romanticism), but without the process of modernization would we have seen the growing nostalgia for the past, the rural, the exotic and the irrational that provided the interest for popular 'traditions'? The project of sociocultural anthropology, including ethnography and ethnology, when it is part and parcel of emerging political and cultural identities, becomes enmeshed in the modernization project and its criticism. And a possible explanation for the inherent split between the motivations for doing anthropology and those for doing ethnology might be that while some students of the rural and the irrational considered it their duty to help eradicate them (Buchowski in this volume describes such a case, when referring to 'the tribe' of positivists in Polish academia), others fought to preserve them.

… and the Complex Relationship between Anthropology and the other Social Sciences

The distinction between anthropology and ethnology is a constant reality in the history of European anthropologies, especially in Eastern Europe. If in recent years the frontiers between the two fields were blurred, many practitioners of the discipline still consider them relevant. The national traditions of the discipline in Croatia, Slovakia, Lithuania and Poland, as reflected in this volume, show ethnology and anthropology in opposition, or at any rate not in collaboration: a 'two-pronged discipline'. Only the chapter on Finland reveals a quieter and more productive relation between these two fields.

Moving further to the east, we note that during the Soviet period 'ethnography' was used as a synonym for ethnology, and at times for sociocultural anthropology. With the 'Soviet era' being a loose category, as revealed by the chapter on Slovakia, the use of the discipline's name and the focus on objects of research varies over time and space as in Western countries. The chapters on Finland, Lithuania, France and Greece, and partly that on Poland, analyse also the relation of anthropology/ethnology to other disciplines such as sociology, folklore or history. It is interesting to note that these relations are either unequal or are characterized by blurred boundaries. Susana de Matos Viegas and João de Pina-Cabral broach the matter more obliquely in their chapter on Portugal, a country that saw the development of a unique combination of empire-building and nationbuilding anthropologies, but struggles to assert its privileged relations to countries such as Brazil and China (its 'empire' components) in order to get noticed and be acknowledged in the national context. It is as if the concept of collaborative or complementary science was unknown to an anthropology that had to assert itself to find its own voice among the social sciences.

We also need to acknowledge today's constitution and fast expansion of new area studies like the anthropology of Eastern Europe, postsocialist studies and the anthropology of Eurasia [START_REF] Barrera-González | Europe[END_REF]; chapters by Buchowski and Ciubrinskas in this volume). The aforementioned new study areas have been established, nurtured and peopled mostly by U.S., British, German and French professional anthropologists working in the region [START_REF] Barrera-González | Europe[END_REF], as funding for these fast-growing research endeavours has come from new foreign-inspired universities established in these countries; private entities like the Wenner-Gren Foundation; and specific research programmes focused on the region set up by the Max Planck Society (mostly via the Max Planck Institute for Social Anthropology) or the French Centre National de la Recherche Scientifique (via the Centre Marc Bloch), for instance. 8 Through these external influences, we also see the looming hierarchies of knowledge and academic authority, and the unawareness or blatant mutual ignorance between local and foreign practices within the discipline of sociocultural anthropology in the European field.

Overall, what the chapters in the volume show is the occurrence of multiple crossings in the formation of most European anthropologies: juxtapositions, overlaps, convergences and divergences of traditions in the development of anthropological theory, method and practice. Many of these intersections testify to the existence of unequal power relations during the past two centuries, which have ended up being reflected in the formation of the discipline. Today, the emergence of a new common scientific playground makes the European field a true laboratory for experimenting with new methods, theories and subject matters for the discipline.

LOOKING TOWARDS THE FUTURE: GOING BEYOND POWER RELATIONS

How we trace intellectual genealogies, what we quote and which lines of reflection we pursue today is likely to influence the shape of tomorrow's anthropology. Today's unequal visibility of distinct European anthropological traditions prompt us to rescue small traditions of anthropology that are bound to disappear if not interrogated and re-evaluated. The 'global' science could become a better science, one in which efforts are joint, or a colonial science, one in which traditions that are not mainstream are erased on the basis of non-conformity to the most successful standards of science. How are intellectual traditions created, and what are the power relations that exist between them? Anthropology, a science of the margins, should be particularly keen not to neglect its own mission. However, this militant argument of academic justice should be complemented by the more utilitarian argument of scientific interest. Understanding different approaches to anthropology is a helpful exercise in cultural relativism and gives a strong impulse to the paradigm change towards a historically sensitive and socially engaged anthropology. In this second section we take up this issue against the background of recent changes in the evaluation of science and academia, and warn about the thin line between the imperative of societal usefulness and the barriers to scientific freedom.

Circulation of Ideas: Who Was First and Who is Borrowing from Whom?

Scholars who were developing ethnology/anthropology worked under influences of extra-national traditions. To study these influences, we need to consider the circulation of ideas and borrowing, and even the eventuality of intellectual theft. The resulting picture is fascinating. Each chapter of this book invites the reader to plunge into the specificity of a different European country. In the introduction we will limit ourselves to raising a few questions that stem from this overview itself.

In most of the chapters on nation-building anthropologies we see that the transmission of anthropological knowledge took place mostly from empire anthropologies to more peripheral non-imperial ones. But one could wonder whether this perception was formed a posteriori on the basis of what remained more visible in theory due to current power relations within academia. If smaller traditions borrowed from 'greater' ones, was it because the national ones were less developed (underdeveloped or backward) or not dominant (i.e., not visible and influential, not able to 'talk to' more powerful traditions) in the hegemonic, notably Anglo-Saxon, academic discourse? At the beginning of the twentieth century, national intellectuals were mostly educated in the imperial metropolises of the time; this trend was resumed at the end of the twentieth century due to the increased circulation of scholars and their attraction to prestigious Western universities. These intellectuals carried throughout their career the influence of their initial training, but this did not prevent them from innovating.

One could ask why such debates between traditions are still important today. The first answer would be that maybe they should be part of the crystallization of the discipline's identity, as they resonate clearly with the difficulties identified by postmodern anthropology in relation to the thin subject/object demarcation line. But maybe these debates are simply due to academics' pragmatic need for getting published or getting a fair amount of academic recognition. These issues are referred to in a number of the chapters, and there are several proposed 'ways out' of the peripheral position: a cosmopolitan anthropology ( Jasna Čapo and Valentina Gulin Zrnić in this volume); an eclectic (cross-fertilizing) anthropology, incorporating ethnological and historicist contributions (Alexandra Bitušíková in this volume); and a hybridity of theories ( Jasna Čapo and Valentina Gulin Zrnić in this volume).

In this competition for recognition, figures like Malinowski and Boas, who gained fame as anthropologists based in the universities of imperial metropolises, are interesting cases. They remained important figures for the anthropological traditions of the countries to which they migrated and where they served as mediators, but did they reciprocally become agents of legitimation for their peripheral traditions of origin? People who were influential within a national tradition carried on the dialogue with the traditions of empire, even if this was in the form of rejection -as in the case of Bromley in Russia. The contrary is seldom true. National traditions do not seem to succeed in superseding their limitations and imposing 'original theory'. The Moscow-Tartu semiotic school is often cited as one of the unique paradigms that 'have made it' to the West. Because of the Western recognition, it is more likely to be considered a great theoretical contribution, as if Western validation was needed to legitimize local reputation. What is valued at some point in scholarly knowledge in the humanities, whether it is generality-universality-systematicity or novel groundbreaking paradigm freshness, prevents or leads to the recognition of intellectuals such as Eliade, Lotman and Bakhtin in the West (these last being valued according to the second criterion). In general it is considered that the periphery has to be twice as knowledgeable, twice as erudite, etc., as the centre to be allowed to speak to the centre critically.

But change often comes from the margins, and this can be applied to anthropology as a whole. Its peripheral character boosted the discipline at times when 'marginal' countries/groups became the forerunners of historic change (decolonization, emancipation and, later, postmodernism). Today, when historical processes are again driven by the centre (a Marxist view would say 'by capital'), the role of anthropology is diminishing. Anthropology could retrieve its 'marginal' vocation by exploring its own diverse voices.

Supporting Societal Modernization Today: Facing the New European Union Standards in Teaching and Research

Over the last decade, changes in European academia have aimed at creating a common European research space [START_REF] Bellier | L'anthropologie dans la politique européenne de recherche[END_REF]. This is what makes our reconsideration of the multiplicity of traditions in anthropology still relevant. The European policymakers come with a particular concept of science and the university, a different version of the requirement of the social relevance (usefulness) of science, as part of a new project of societal modernization. The university is imagined today as a place where students are made 'immune' to unemployment by their being provided with marketable skills. The academy is thus conceptualized as a reservoir of knowledge that is usable for economic development and can directly affect the affluence and wellbeing of people. It is also considered part of nationalist (or European Unionist) politics of securing oneself the best place in the international (global) competition for economic and political domination. Thus there is some continuity between EU-commissioned and empire-commissioned research in the colonial period.

The idea of preparing students to enter the job market is not faulty, yet it creates false expectations at two levels: first, that the job market generally needs the skills that should be developed at university level; and second, that students, in the course of their studies, acquire 'useful' knowledge that has overtones of 'true' knowledge. The margin of uncertainty, reflexivity and doubt present in social science and humanities knowledge shrinks dramatically. The arguments that the academy -anthropology in particular -should become more engaged with the real world and acquire more prosocial stances are well grounded (e.g., [START_REF] Eriksen | Engaging Anthropology[END_REF]Ribeiro and Escobar 2006). Viazzo's chapter on Italy in this volume points out that 'autistic survival' is not a viable option, that anthropology should be directed to the needs of its students and to the needs of societies. Yet, the wish to serve society and to cater for students' needs is not equivalent to the claims of contemporary neoliberal political and corporate actors, who, by and large, postulate that the university shall serve the market. Advocates of 'public anthropology' distance themselves from the statement that anthropology (or any other humanities discipline) could be a panacea for repairing the malfunctioning of the late capitalist world. Rather, they look for ways of making anthropology a more integral part of today's society. As for sociology, Michael [START_REF] Burawoy | The Last Positivist[END_REF] argued that economic and political institutions had a disproportionally large influence on the outlook of the discipline, and suggested that civil society institutions should be given more opportunities to shape the research agenda. How anthropologists might act in order to engage with the public sphere, without being absorbed by ideologically loaded projects they do not want to be part of, are procedures that are still to be written down. The tradition of searching for such formulas is rich; among other sources, the journal Anthropology in Action provides a great deal of insight into the endeavours of applied anthropology in Europe.

The difficulties experienced by the humanities in attempting to preserve their identity and their very existence have been well described. On the one hand, insecurities related to the specificity of method (participant observation), the postmodernist turn [START_REF] Clifford | Writing Cultures: Poetics and Politics of Ethnography[END_REF] and the need to face the colonial entanglements of anthropology [START_REF] Pels | What Has Anthropology Learned from the Anthropology of Colonialism?[END_REF]) have inserted hesitation, reflexivity and avoidance of self-glorification at the disciplines' core [START_REF] Descola | On Anthropological Knowledge[END_REF]. On the other hand, the change brought from the outside under the name of university reform [START_REF] Romano | Studying Anthropology in the Age of University Reform[END_REF] or 'audit culture' [START_REF] Shore | Audit Culture and Anthropology: Neo-Liberalism in British Higher Education[END_REF] has been contributing to the marginalization of all humanities, including anthropology.

However, the situation across Europe is asymmetrical. The countries with shorter or more troubled traditions of institutional development of the discipline, such as Bulgaria and Poland, face more severe pressures than those where anthropology has existed as a fully fledged academic discipline for a longer period. For instance, when quantitative measurements of academic excellence are developed in a haphazard and non-transparent fashion (cf. [START_REF] Brenneis | Anthropology in and of the Academy: Globalization, Assessment and our Field's Future[END_REF], national anthropologies that use 'smaller' languages (such as Lithuanian or Slovak) automatically find themselves in a disadvantageous position compared with those whose language base is wider (such as English or Portuguese) [START_REF] Wagner | Selektywna analiza problemu publikacji humanistów i przedstawicieli nauk społecznych w języku angielskim[END_REF].

Generally, institutional change is driving anthropology/ethnology to become a new type of science, which is inadequately built on the model of hard sciences in which all communications and publications are in English, and all publishing is in peer-reviewed journals rather than in books and is signed by whole teams of researchers. None of these criteria are favourable to anthropology, with its monographs, its literary style and its individually performed in-depth fieldwork. There is some resistance to this trend, but the possibility of resisting is more open to those scholars who are from the 'bigger' traditions, supported by richer economies. Scholars from the 'new' Europe often have to be more complacent out of fear of being excluded from European funding opportunities that are not adequately paralleled by national funding.

The issue of how academic knowledge is produced and disseminated is crucial today, when publications are the first means of evaluating science and the first token of prestige. Publishing is pivotal: whose hands are on the levers of publishing? What are the processes for getting into good publishing houses? What is the gap between the written rules and the practical (tacit) knowledge or practice as such? This matter is very much related to the issue of access to audiences, and the internal differentiation of audiences in anthropological writing: audiences that evaluate and enable, or not, career development; audiences that speak or do not speak the same 'language' as the author. By 'language' we refer here to the language of constructing the scholarly argument, the 'canon' of literature one refers to as well as a set of ethical and epistemological sensibilities that members of a discursive community share. We add to this the importance of embeddedness in networks of academic practice, which could be central or peripheral. Scholarly cooperation is starting to bear the signs of business monopoly and it is extremely difficult for a new player to enter the game. In the context of rapid technological development that makes information, including anthropological knowledge, ever more vast and seemingly ever more available, marketing and networking mechanisms often define what will be noticed, selected for scholarly debate and recognized -not academic excellence. Many scholars in peripheral universities publish a lot of books in local publishing houses, and are not able to 'market' them properly. Some of them do not even undergo a fully-fledged review process. In these cases, publication is no longer a vehicle of scientific advancement; it is a dead end. These changes -however minuscule or particular they may seem -are a sign of the continued and perhaps increasing (or increasingly obvious) dependence of science (academy) on politics and the economy. It may be that they signal a shift in modernization perceptions. The Enlightenment ideal of science that is ruled by its internal logic gives way to a project of science that is financially efficient and serves particular political or economic goals. This can also be seen as a particular backlash of modernization rhetoric, since the overarching goal of a rational actor controlling the external environment has come full circle and ended up being executed on science itself. The criteria that are used in the evaluation of science today come from different and incompatible social fields (be it economics or politics).

More particularly, the neoliberal rhetoric of European research policy results in a changing outlook for sciences and humanities. It positions scholars so that they need to constantly prove their usefulness and their ability to positively influence national and European economies in a bureaucratic fashion. The case of the Research Assessment Exercises in the United Kingdom described by [START_REF] Shore | Audit Culture and Anthropology: Neo-Liberalism in British Higher Education[END_REF] is representative of European science in general. The possibilities of resistance are limited, since research funding is heavily dependent on these evaluations, as [START_REF] Shore | Beyond the Multiversity: Neoliberalism and the Rise of the Schizophrenic University[END_REF] demonstrates in his analysis of the Performance Based Research Fund introduced in New Zealand. The emphasis on efficiency puts inadequate pressure on researchers' productivity and compromises the significance of their findings (e.g., more innovative, 'risky' and less predictable research designs are avoided, longer-term projects are pursued less often, etc.). A few chapters in the volume devote space to this new predicament (notably those on Greece and Portugal). The regard towards the future of anthropology is sometimes optimistic, sometimes pessimistic. The optimistic view comes from discipline practitioners in countries where anthropology has succeeded in finding a niche. The pessimistic view is often linked to institutional pressure to join with other humanities disciplines, to dismantle departments, and to secure more students to justify their existence.

Science and the Market: Ethnographic Notes on the Entrepreneurial University

The above state of affairs is neither new nor unique to the practice of anthropology, but it is worth mentioning, given its impact on the content of science. Due to either academic capitalism [START_REF] Hoffman | The New Tools of the Scientific Trade: Contested Knowledge Production and the Conceptual Vocabularies of Academic Capitalism[END_REF] or the schizophrenic university [START_REF] Shore | Beyond the Multiversity: Neoliberalism and the Rise of the Schizophrenic University[END_REF], depending on the interpretation we favour, anthropology does change. The way in which Hoffman uses Bourdieu's terminology to explain the workings of academic capitalism is instructive. He suggests that 'an increase in market-orientation has not displaced more traditional academic practices and values but facilitated the development of new conceptual vocabularies that are subtly remaking academic practice and culture' (Hoffman 2011: 441). Hoffman distinguishes four such domains: market-oriented entrepreneurialism, external consulting work, consumer-oriented research and interdisciplinarity (cf. [START_REF] Strathern | Experiments in Interdisciplinarity[END_REF]. The tensions between these domains and the contradictory priorities that they set for scholars contribute to the new divisions in the academy. One of these is a division between disciplines that are close to and those that are 'far removed from market potential' (Hoffman 2011: 457), like biochemistry and art history respectively. When a discipline that is further distanced from the market (as anthropology is) is made to adopt the vocabulary of entrepreneurialism, it causes a greater and more painful stretching of the discipline's identity than in the case of one that is closer. In Chevalier's chapter on French anthropology, the issue of dependence on the economic sphere acquires an interesting twist. She writes about the role museums play in the development of the profession. As increasingly commercial institutions, museums need to follow the aesthetics of mass consumption in their endeavours. This forces anthropologists who cooperate with museums to direct their research or their display of results in the direction of 'mass digestible' aesthetic objects. This is one example of how various domains (market, consumption, aesthetics and materiality) interact to shape the scientific discipline.

Paradoxically, these processes also give rise to new sensitivities and imperatives that are not necessarily detrimental to science but rather bring it into new societal contexts. Hoffman gives an example of a 'wide variety of civic engagement and community collaboration' resulting from the influence of 'external consulting work' vocabulary [START_REF] Hoffman | The New Tools of the Scientific Trade: Contested Knowledge Production and the Conceptual Vocabularies of Academic Capitalism[END_REF]. Since in Bourdieu's original theory the issue of a given field's autonomy is pivotal, the issue of autonomy also surfaces in the discussion of the dependence of science and the academy on other fields: do they have autonomy now; have they ever had autonomy; should they have it; is it feasible that they will have it at least partially; and what logics and vocabularies will be at work, if a degree of autonomy is achieved?

In one important sense, however, science cannot completely divorce itself from the market: it is a field of professional activity; scholars live off their profession. Thus, when considering how anthropology is practised today in Europe we could not overlook the fact that the academy is a 'place' where anthropologists work. It is important, therefore, to consider how their workload is distributed between academic and administrative tasks in the context of the grant-based funding of science. Employment conditions have to be analysed in conjunction with research-funding conditions. In her chapter, Bitušíková tries to explain why most Slovak anthropologists do not work in faraway lands, by pointing to the low level of funding available for overseas research, or for any research activities in fact. Doing online ethnography or anthropology at home becomes a matter of necessity rather than a choice.

We can also look at how precarious employment influences the type of research that is carried out (i.e., what kind of ethnography can be carried out if a researcher is employed on a one or two-year contract with no prospect of extension?). The rising numbers of anthropology graduates increase competition for university positions in the discipline, even in such established traditions as the British one (Kuper 2005). University employment has become notoriously precarious in Germany, where many anthropologists with qualifications as high as that of Habilitated Doctor can count on only short-term contracts, and where many decide to quit academia due to the impossibility of attaining longer-term posts.

The wider availability of higher education across Europe during the last decades of the twentieth century caused university student numbers to swell. In the countries of Eastern and Central Europe, the demand for higher education increased after 1989; the establishment of numerous private universities met this demand. This niche was saturated, however. In the second decade of the twenty-first century, demographic factors (the lower numbers of prospective students) threaten the existence of many departments and institutes, especially in the humanities and social sciences. This is the case in Poland and Bulgaria, for instance, where anthropology departments in private but also public universities are experiencing hardships, and academics who work there fear unemployment.

Universities have always been dependent on politics and the economy in one way or another, but we may be witnessing the end of a unique arrangement in Western Europe, in which universities have enjoyed a considerable amount of autonomy. In the chapter on Portuguese anthropology, the authors suggest that this may be an effect of the recession in Europe. It has also been voiced that it might be linked to bureaucratization and centralization caused by European integration (Bellier 2008). Yet again, we need to differentiate at the European scale, because the relative autonomy from the political field (e.g., in terms of curriculum development) that has been the rule for French and Italian universities since the late 1960s and early 1970s was achieved in Lithuania, Poland and Croatia only in the early 1990s. While the increased freedom of theorizing after 1989 is indisputable, the postcolonial critique of transformations in the Eastern and Central European academy demonstrates that speaking of limitless freedom would be naive, since Western thought has an added symbolic value compared to the others, which is unrelated to its academic merit [START_REF] Buchowski | The Specter of Orientalism in Europe: From Exotic Other to Stigmatized Brother[END_REF][START_REF] Warczok | Bourdieu Recontextualized: Redefinitions of Western Critical Thought in the Periphery[END_REF]. In places where anthropology departments are only just emerging, academic freedom is being achieved at the very moment when the existence of the academy is under an immense threat because of a dramatic lack of funds.

CONCLUSION

The volume that we are presenting to readers is not being thought of as an exhaustive catalogue of all traditions in European sociocultural anthropology and ethnology. Rather, we see our goal as that of juxtaposing traditions 'big' and 'small', developed as part of the processes of nation-building and/or empire-building and concerned with the proximate or with the distant other. The chapters collected in this volume demonstrate that national traditions of sociocultural anthropology and ethnology are hardly ever independent of other traditions; they are usually hybrids that have grown out of borrowings and mutual influences. It appears that the disciplines would benefit greatly from viewing this latter feature as their strength. Yet the socio-economic context of academic knowledge remains by and large hostile to hybridity.

Research on what is hybrid and mobile in national traditions could become a future venue for research in the history of anthropology.

We share the view that anthropology and ethnology should attempt to find ways of actively engaging with the world outside of the academy (cf. Hann 2009) and stop being 'autistic' (Viazzo, this volume). Yet, on the basis of the collected evidence we humbly acknowledge that the roads to public anthropology and to applying ethnological knowledge to social practice are bumpy. To start with, the epistemological commitment to avoiding ethnocentrism dictates that the ways of defining 'public good' should be treated as 'neither common nor sensible', to paraphrase Herzfeld's definition of common sense (2001: 1). It is, therefore, obvious that anthropology and ethnology -more than any other academic discipline -should care about being reflexive. In a recent essay, Johannes [START_REF] Fabian | Ethnography and Intersubjectivity: Loose Ends[END_REF] suggested that this reflexivity should be intersubjective rather than critical. We thus propose considering this volume as an exercise in various traditions of anthropology and ethnology speaking and listening to each other.

Andrés Barrera-González, has received a Ph.D. in Political Science and Sociology and is Associate Professor of Social Anthropology at the University Complutense of Madrid. He has published on issues of inheritance and family systems, language politics and policies, and cultural identities in Spain. At present he is involved in research and writing in the history of anthropology and ethnology in Spain and the Hispanic world.

Monica Heintz (Ph.D. Cambridge) is Associate Professor in Social Anthropology at the University of Paris Nanterre. She is the author of "Be European, Recycle Yourself!": Changing Work Ethic in Romania, editor of Weak State, Uncertain Citizenship: Moldova, and The Anthropology of Moralities, and co-editor of the volume Transitions Historiques.

Anna Horolets is an Associate Professor at the Chair of Social Anthropology, University of Gdańsk. She has recently published a monograph on niche tourism from Poland to the former Soviet Union (2013) and articles on migrants' leisure. She is an editor for social anthropology of the Polish peer-reviewed journal Studia Sociologiczne. Notes 1. 'National' is used here as shorthand for a far more complex state of affairs, which each chapter will consider in more detail. For instance, it quickly became clear to us that it was irrelevant to consider German anthropology as restricted to the anthropology practised within the country of Germany, and that the unit that would make sense intellectually today for the development of the discipline included all German-speaking countries in Europe (Germany, Austria and Switzerland). 2. 'Inclusive' refers here to considering Volkskunde and Völkerkunde, major and minor national traditions, equally. Nevertheless, the concept is also relevant in other contexts and senses (Handler 2000(Handler , 2006)). 3. It is interesting to note that imperial authorities commissioned the ethnographic surveys and ethnological research carried out in Russia's eastern confines via the Russian Academy of Sciences (Vermeulen 2008: 1-23). On the contributions made by German-speaking countries to the development of anthropology (Ethnologie) see also: Stocking (1996); [START_REF] Barth | One Discipline, Four Ways: British, German, French, and American Anthropology[END_REF]; and John Eidson in this volume. 4. The supporting argument is that The History from the time of the Greco-Persian wars in the fifth century BC incorporates descriptions of the diversity of the nations, peoples, customs and cultures that Herodotus encountered on his travels, or came to know about from either oral (including folklore and myth) or written sources. The History is also a dramatic account of the epic confrontation between the perceived Greek civility and Persian despotism. 5. Captain Vladimir K. Arsenyev carried out several military-exploratory expeditions to the far east, north of Vladivostok. As a result of these expeditions he wrote travel and exploration narratives (some of them published posthumously in 1937 under the title In the Sikhote-Alin Mountains), as well as books about the geography and ethnography of the lands he explored. Arsenyev's most famous and justly acclaimed work is the narrative of his expeditions to the Ussurian taiga, with a small party of soldiers, and with Dersu Uzala, a local hunter, as his guide and close collaborator. 6. An illustration of the unfavourable environment in which Russian scholars have had to work and develop their careers at different times in history is the law passed by the Duma in 2013, which imposed a thorough reorganization of the Russian Academy of Sciences, in which anthropology (in its diverse local denominations) has had a significant institutional presence since the eighteenth century. 7. We refer here to both the actual and the projected/attempted empires, to compare Portuguese and French colonial empires with the late colonial ambitions of Germany. 8. The Max Planck Institute for Social Anthropology was founded in 1999 in Halle (Saale), former East Germany. The inauguration of its permanent buildings a few years later was marked by the convening of a series of lectures delivered by prominent anthropologists, entitled 'Four Traditions in Anthropology' [START_REF] Barth | One Discipline, Four Ways: British, German, French, and American Anthropology[END_REF]).


Pascal Préa
email: pascal.prea@lis-lab.fr

François Brucker
email: francois.brucker@lis-lab.fr

Interval Hypergraphs and Catalan Numbers *

An interval hypergraph is a hypergraph H = (V, E) such that there exists an linear order σ (which is said to be compatible) on V such that, when V is sorted along σ, every hyperedge is an interval of V . A interval cover of a set V is an interval hypergraph H = (V, E) such that e∈E e = V and ∀e, e ∈ E, e ⊂ e . In this note, we show that:

• Nearly all interval hypergraphs have only two compatible orders.

• The number of interval covers of {1, . . . , n} is the Catalan number Cn = 1 n+1 2n n .

keywords : Interval hypergraphs, Catalan numbers, PQ-trees, Robinson dissimilarities.

Definitions and notations

A hypergraph is a couple H = (V, E) where V is a finite set whose elements are vertices and E ⊆ 2 V is the hyperedge set. A hypergraph H = (V, E) is an interval hypergraph if there exists a compatible (linear) order σ of V such that, when V is sorted along σ, all hyperedges are intervals. A interval hypergraph H = (V, E) is a interval cover of V if e∈E e = V and ∀e, e ∈ E, e ⊂ e . For V ⊂ V , the restriction of H = (V, E) to V is the hypergraph H| V = (V , E ) where E = {e ∩ V : e ∈ E}.

A PQ-tree T on a set V is a tree that represents a set of permutations on V , and if H = (V, E) is an interval hypergraph, then the set of all compatible orders of H can be represented by a PQ-tree [START_REF] Booth | Testing for the Consecutive Ones Property, Interval Graphs and Graph Planarity Using PQ-Tree Algorithm[END_REF][START_REF] Préa | An Optimal Algorithm to Recognize Robinsonian Dissimilarities[END_REF]. The leaves of T are the elements of V , and the nodes of T are of two types: the P-nodes and the Q-nodes. We use the general convention of writing that is to represent P-nodes by circles, and Q-nodes by rectangles. On a P-node, one can apply any permutation of its children (equivalently, its children are not ordered). The children of a Q-node are ordered, and the only permutation we can apply on them is to reverse the order. For instance, the PQ-tree of figure 1 represents the set of permutations {(1,2,3,4,5), (1,3,2,4,5), (2,1,3,4,5), (2,3,1,4,5), (3,1,2,4,5), (3,2,1,4,5), (5,4,1,2,3), (5,4,1,3,2), (5,4,2,1,3), (5,4,2,3,1), (5,4,3,1,2), (5,4,3,2,1)}.

We say that a PQ-tree is flat if it has only one internal node, which is a Q-node. A flat PQ-tree represents only two permutations. Similarly, an interval hypergraph is flat if it has only two compatible orders, i.e. if its PQ-tree is flat. Conversely, a PQ-tree with one internal node, which is a P-node, is said to be universal. A universal PQ-tree represents all the permutations on S.

A dissimilarity on a finite set V is a symmetric function d : V × V → R + such that d(i, j) = 0 if and only if i = j. Dissimilarities can be seen as a generalization of distances and can be represented by symmetric matrices on R + with a null diagonal. For a dissimilarity d on a set V and δ ∈ R, the graph In the rest of this paper, we will only consider hypergraphs with vertex set V = {1, . . . , n} and we will suppose that, if H is an interval hypergraph, then (1, . . . , n) is one of its compatible orders. We will denote the number of interval hypergraphs on {1, . . . , n} by I n , the number of flat interval hypergraphs by F n and the Catalan number

G δ d = (V, E δ d ) with xy ∈ E δ d ⇐⇒ d(x, y) ≤ δ is a threshold graph of d.
1 n+1 2n n by C n .
2 Results on interval hypergraphs

Claim 1. I n = 2 n(n+1)/2 .
Proof. Since an interval on {1, . . . , n} is either a pair of elements (its extremities) or a singleton, there are n(n + 1)/2 interval in {1, . . . , n}.

Theorem 1. lim n→∞ F n /I n = 1.
Proof. Let H = (V, E) be an interval hypergraph. Suppose that its PQ-tree T H has an internal node α, different from the root of T H , and that the leaves under α are i, . . . , i + k. We have 1 < k < n -i and we set V α := {i, . . . , i + k}.

For every permutation σ represented by T H , V α is an interval of V and, if for some e ∈ E, there exists x ∈ e ∩ V α and y ∈ e \ V α , then V α ⊂ e. So H is entirely determined by H| Vα and H| (V \Vα)∪{i} and thus the number of interval hypergraphs with a node like α (i.e. such that the leaves under it are i, . . . , i + k) as internal node of their PQ-tree is

I [k] n := I k • I n-k+1
. This value is maximum for k = 2 and we have I [START_REF] Chepoi | Recognition of Robinsonian Dissimilarities[END_REF] n = 2 n(n-1)/2+3 . So the proportion of interval hypergraphs having a PQ-tree with a node like α as leftmost internal node is ≤ 1 2 n-3 . There are less than (n -1) 2 possible choices for the type of α (at most n -1 choices for i and n -1 choices for k), so the proportion of interval hypergraphs on {1, . . . , n} which are compatible with a PQ-tree having internal nodes tends to 0 when n tends to ∞. If the PQ-tree of an interval hypergraph H is universal, the hyperedges of H are either singletons or V . So there are only 2 n+1 interval hypergraphs whose PQ-tree is universal, and the result follows.

Note that, even if we do not impose (1, . . . , n) to be a compatible order, nearly all interval hypergraphs have only two compatible orders.

Theorem 2. The number of interval covers of {1, . . . , n} is C n .

Proof. There are C n lattice paths in Z × Z from (1, 1) to (n, n) with steps (0, 1), (1, 0) and (1, 1) never going below the line y = x and such that steps (1, 1) only appear on the line y = x (Exercice 52 of [START_REF] Stanley | Catalan Numbers[END_REF]). In such a path, a summit is a point with neither a step (1, 0) just before it nor a step (0, 1) just after.

If we associate with each summit (i, j) the interval [i, j] (see Figure 2), we build a one-to-one correspondence between these paths and interval covers of {1, . . . , n}.

x y

• • a • • • • b • • • c • • • d • • • • • e • • f • • g • • • • • I a I c I e I g I b I d I f
Figure 2: A lattice path on Z × Z from (1, 1) to (13, 13) with summits a, b, . . . , g and the corresponding intervals I a , I b , . . . , I g , which form an interval cover of the points (1, 1), (2, 2), . . . (13, 13).

Robinson dissimilarities

A dissimilarity d on a finite set V is Robinson [START_REF] Robinson | A Method for Chronologically Ordering Archeological Deposits[END_REF] if there exists a linear order σ on V (which is said to be compatible) such that, when [START_REF] Diday | Orders and Overlapping Clusters by Pyramids[END_REF][START_REF] Durand | One-to-One Correspondences in Pyramidal Representation: a Unified Approach[END_REF]; in addition, d and (V, C d ) have the same set of compatible orders [START_REF] Préa | An Optimal Algorithm to Recognize Robinsonian Dissimilarities[END_REF]. We will identify two dissimilarities d and

V is ordered along σ, i < j < k =⇒ d(i, j) ≤ d(i, k) and d(j, k) ≤ d(i, k). A dissimilarity d on V is Robinson if and only if (V, C d ) is an interval hypergraph
d if C d = C d ;
and, as for interval hypergraphs, we will suppose that V = {1, . . . , n} and (1, . . . , n) is a compatible order.

Claim 2. The number of Robinson dissimilarities on V is 2 n(n-1)/2-1

Proof. V ∪ {V } is always a subset of C d , so the number of intervals that can be, or not, in

C d is n(n -1)/2 - 1.
Theorem 3. The number of Robinson dissimilarities on {1, . . . , n} with values in {0, 1, 2} is C n -1.

Proof. When d takes its values in {0, 1, 2}, the relation R on V defined by iRj ⇐⇒ d(i, j) ≤ 1 is reflexive, symmetric and such that if 1 ≤ i < j < k ≤ n, and iRk, then iRj and jRk. There are C n such relations on V (Exercice 187 of [START_REF] Stanley | Catalan Numbers[END_REF]). Since the dissimilarities defined by i = j =⇒ d(i, j) = 1 and by i = j =⇒ d(i, j) = 2 are equivalent, the result follows.

If we represent a Robinson dissimilarity d by a matrix with a horizontal diagonal (see Figure 3), we get "stacks" of lattice paths (like the one in Figure 2) with a "peak" in foreground. If d takes its values in {0, . . . , k}, the stack is made of k lattice paths (including the peak in foreground); equivalently, C d does not contain e 1 , e 2 , . . . e k with ∀1 ≤ i ≤ k, 1 < |e i | < n and e 1 ⊂ e 2 ⊂ . . . ⊂ e k . Table 1 shows the number of

Conclusion

Our original goal was to prove that nearly all Robinson dissimilarities have a flat PQ-tree (a direct consequence of Claim 2 and of the proof of Theorem 1), which was intended to be a first step toward the determination of the average complexity of algorithms like those of [START_REF] Chepoi | Recognition of Robinsonian Dissimilarities[END_REF] or [START_REF] Laurent | Similarity-First Search: a New Algorithm with Application to Robinsonian Matrix Recognition[END_REF]. This lead us to lattice paths, and thus to a combinatorial interpretation of Catalan numbers (Theorem 2). This interpretation, although very simple, natural and easy to prove, seems curiously to have been unknown until now.

Figure 1 :

 1 Figure 1: A PQ-tree

Figure 3 :

 3 Figure 3: Robinson dissimilarities represented by matrices with a horizontal diagonal.Robinson dissimilarities on {1, . . . , n} taking their values in {0, . . . , k} for small values of k and n. Sequences for k = 3, 4, 5 match no sequence in OEIS[START_REF]OEIS: The On-Line Encyclopedia of Integer Sequences[END_REF] and we know no formula for them.

Table 1 :

 1 Number of Robinson dissimilarities on {1, . . . , n} that take their values in {1, . . . , k} for small values of n and k ∈ {2, 3, 4, 5, ∞}. The boxes with // needed too much computation time to be filled.

	n \ k	2	3	4	5	∞
	2	1	1	1	1	1
	3	4	4	4	4	4
	4	13	32	32	32	32
	5	41	266	512	512	512
	6	131	2254	9938	16384	16384
	7	428	19934 208717 708314	1048576
	8	1429 185383	//	//	134217728
	9	4861	//	//	//	34359738368
	n	C n -1	?	?	?	2 n(n-1)/2-1

This work was supported in part by ANR project DISTANCIA (ANR-17-CE40-0015).