{"id":"https://openalex.org/W2163496513","doi":"https://doi.org/10.37236/2193","title":"Some Relational Structures with Polynomial Growth and their Associated Algebras I: Quasi-Polynomiality of the Profile","display_name":"Some Relational Structures with Polynomial Growth and their Associated Algebras I: Quasi-Polynomiality of the Profile","publication_year":2013,"publication_date":"2013-04-09","ids":{"openalex":"https://openalex.org/W2163496513","doi":"https://doi.org/10.37236/2193","mag":"2163496513"},"language":"en","primary_location":{"id":"doi:10.37236/2193","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2193","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p1/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p1/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074634772","display_name":"Maurice Pouzet","orcid":"https://orcid.org/0000-0003-3348-3822"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I4210104796","display_name":"Institut Camille Jordan","ror":"https://ror.org/01ekw7f87","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210104796","https://openalex.org/I4405259976","https://openalex.org/I48430043"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Maurice Pouzet","raw_affiliation_strings":["Universit\u00e9  Claude-Bernard, Lyon1","ICJ - Institut Camille Jordan (B\u00e2t. Jean Braconnier 43 bd du 11 novembre 1918 69622 VILLEURBANNE CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9  Claude-Bernard, Lyon1","institution_ids":["https://openalex.org/I100532134"]},{"raw_affiliation_string":"ICJ - Institut Camille Jordan (B\u00e2t. Jean Braconnier 43 bd du 11 novembre 1918 69622 VILLEURBANNE CEDEX - France)","institution_ids":["https://openalex.org/I4210104796"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003371779","display_name":"Nicolas M. Thi\u00e9ry","orcid":"https://orcid.org/0000-0002-2735-8921"},"institutions":[{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I3019441195","display_name":"Laboratoire de Math\u00e9matiques d'Orsay","ror":"https://ror.org/03ab0zs98","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I3019441195"]},{"id":"https://openalex.org/I4210144804","display_name":"Laboratoire de Recherche en Informatique","ror":"https://ror.org/04e3ktk27","country_code":"FR","type":"facility","lineage":["https://openalex.org/I102197404","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210144804","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nicolas Marc Thi\u00e9ry","raw_affiliation_strings":["Univ Paris-Sud, Laboratoire de Math\u00e9matiques d'Orsay,\r\nOrsay, F-91405; CNRS, Orsay, F-91405","LMO - Laboratoire de Math\u00e9matiques d'Orsay (B\u00e2timent 307, rue Michel Magat, Facult\u00e9 des sciences, Universit\u00e9 Paris-Saclay, 91405 Orsay C\u00e9dex. - France)","GALaC - LRI - Graphes, Algorithmes et Combinatoire (LRI) (Universit\u00e9 Paris-Sud ; b\u00e2t. 650 Lovelace ; 91405 Orsay Cedex - France)"],"affiliations":[{"raw_affiliation_string":"Univ Paris-Sud, Laboratoire de Math\u00e9matiques d'Orsay,\r\nOrsay, F-91405; CNRS, Orsay, F-91405","institution_ids":["https://openalex.org/I3019441195","https://openalex.org/I102197404","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"LMO - Laboratoire de Math\u00e9matiques d'Orsay (B\u00e2timent 307, rue Michel Magat, Facult\u00e9 des sciences, Universit\u00e9 Paris-Saclay, 91405 Orsay C\u00e9dex. - France)","institution_ids":["https://openalex.org/I3019441195","https://openalex.org/I277688954"]},{"raw_affiliation_string":"GALaC - LRI - Graphes, Algorithmes et Combinatoire (LRI) (Universit\u00e9 Paris-Sud ; b\u00e2t. 650 Lovelace ; 91405 Orsay Cedex - France)","institution_ids":["https://openalex.org/I102197404","https://openalex.org/I4210144804"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5074634772"],"corresponding_institution_ids":["https://openalex.org/I100532134","https://openalex.org/I4210104796"],"apc_list":null,"apc_paid":null,"fwci":2.8203,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.89260658,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"20","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.701705276966095},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.580971360206604},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5784702301025391},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.5780460238456726},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5587956309318542},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5442892909049988},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5211972594261169},{"id":"https://openalex.org/keywords/hilbert-series-and-hilbert-polynomial","display_name":"Hilbert series and Hilbert polynomial","score":0.4579760730266571},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4210679829120636},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35855087637901306},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30919602513313293},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.12541651725769043},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08985266089439392},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06834670901298523}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.701705276966095},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.580971360206604},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5784702301025391},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.5780460238456726},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5587956309318542},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5442892909049988},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5211972594261169},{"id":"https://openalex.org/C57033185","wikidata":"https://www.wikidata.org/wiki/Q5761236","display_name":"Hilbert series and Hilbert polynomial","level":3,"score":0.4579760730266571},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4210679829120636},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35855087637901306},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30919602513313293},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.12541651725769043},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08985266089439392},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06834670901298523},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.37236/2193","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2193","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p1/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1402.3090","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1402.3090","pdf_url":"https://arxiv.org/pdf/1402.3090","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.400.904","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.400.904","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.inria.fr/docs/00/83/38/54/PDF/13-Pouz-Thie.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00833854v1","is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-00833854","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Electronic Journal in Combinatorics","raw_type":"\\ninfo:eu-repo/semantics/article\\n"},{"id":"pmh:oai:HAL:hal-01121195v1","is_oa":false,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-01121195","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"\\nISSN: \\n1077-8926","raw_type":"\\ninfo:eu-repo/semantics/article\\n"},{"id":"pmh:oai:HAL:hal-01121195v2","is_oa":true,"landing_page_url":"https://hal.science/hal-01121195","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The Electronic Journal of Combinatorics, 2013, 20 (2), 35pp. ⟨10.37236/2193⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.37236/2193","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2193","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p1/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320314997","display_name":"Strong","ror":"https://ror.org/041vyzr56"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2163496513.pdf","grobid_xml":"https://content.openalex.org/works/W2163496513.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W3667550","https://openalex.org/W116888106","https://openalex.org/W417925666","https://openalex.org/W1514324498","https://openalex.org/W1599335667","https://openalex.org/W1606804863","https://openalex.org/W1640107250","https://openalex.org/W1650977650","https://openalex.org/W1827762026","https://openalex.org/W1904629195","https://openalex.org/W1967082722","https://openalex.org/W1967222652","https://openalex.org/W1980775575","https://openalex.org/W1981803420","https://openalex.org/W1992923277","https://openalex.org/W2015773946","https://openalex.org/W2034385828","https://openalex.org/W2052438272","https://openalex.org/W2060284228","https://openalex.org/W2061432895","https://openalex.org/W2076508310","https://openalex.org/W2079167981","https://openalex.org/W2083811053","https://openalex.org/W2091015960","https://openalex.org/W2097591144","https://openalex.org/W2125013303","https://openalex.org/W2126209209","https://openalex.org/W2138740649","https://openalex.org/W2154214744","https://openalex.org/W2163841074","https://openalex.org/W2166736885","https://openalex.org/W2167567843","https://openalex.org/W2167928772","https://openalex.org/W2319466955","https://openalex.org/W2331307912","https://openalex.org/W2797717882","https://openalex.org/W2914659449","https://openalex.org/W2949176902","https://openalex.org/W2950647997","https://openalex.org/W3023266761","https://openalex.org/W4210972826","https://openalex.org/W4250501683","https://openalex.org/W4253748139","https://openalex.org/W4285719527","https://openalex.org/W4290004362","https://openalex.org/W4361793181","https://openalex.org/W4384817650","https://openalex.org/W6684739701"],"related_works":["https://openalex.org/W3194471551","https://openalex.org/W4375956809","https://openalex.org/W1581373162","https://openalex.org/W2784911598","https://openalex.org/W4297950433","https://openalex.org/W4287023968","https://openalex.org/W4288279572","https://openalex.org/W1973978937","https://openalex.org/W4247734921","https://openalex.org/W1525049041"],"abstract_inverted_index":{"The":[0],"profile":[1],"of":[2,22,24,46,95,102],"a":[3,47,67,80,111,126],"relational":[4,76],"structure":[5,77],"$R$":[6,25,78],"is":[7,42,109,124,130],"the":[8,17,28,43,53,75,100,115],"function":[9,45],"$\\phi_R$":[10,36,108,123],"which":[11],"counts":[12],"for":[13],"every":[14],"integer":[15],"$n$":[16],"number":[18],"$\\phi_R(n)$,":[19],"possibly":[20],"infinite,":[21],"substructures":[23,32],"induced":[26],"on":[27,121],"$n$-element":[29],"subsets,":[30],"isomorphic":[31],"being":[33],"identified.":[34],"If":[35],"takes":[37],"only":[38],"finite":[39,81,96],"values,":[40],"this":[41,63,71,113],"Hilbert":[44],"graded":[48,89],"algebra":[49,55],"associated":[50],"with":[51],"$R$,":[52,122],"age":[54],"$KA(R)$,":[56],"introduced":[57],"by":[58,132],"P.":[59],"J.":[60],"Cameron.":[61],"In":[62],"paper":[64],"we":[65],"give":[66],"closer":[68],"look":[69],"at":[70],"association,":[72],"particularly":[73],"when":[74,128],"admits":[79],"monomorphic":[82],"decomposition.":[83],"This":[84],"setting":[85],"still":[86],"encompass":[87],"well-studied":[88],"commutative":[90],"algebras":[91],"like":[92],"invariant":[93],"rings":[94,101],"permutation":[97],"groups,":[98],"or":[99],"quasi-symmetric":[103],"polynomials.":[104],"We":[105],"prove":[106],"that":[107],"eventually":[110,125],"quasi-polynomial,":[112],"supporting":[114],"conjecture":[116],"that,":[117],"under":[118],"mild":[119],"assumptions":[120],"quasi-polynomial":[127],"it":[129],"bounded":[131],"some":[133],"polynomial.":[134]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}