{"id":"https://openalex.org/W2777599242","doi":"https://doi.org/10.37236/9575","title":"On the Matchings-Jack and Hypermap-Jack Conjectures for Labelled Matchings and Star Hypermaps","display_name":"On the Matchings-Jack and Hypermap-Jack Conjectures for Labelled Matchings and Star Hypermaps","publication_year":2024,"publication_date":"2024-07-26","ids":{"openalex":"https://openalex.org/W2777599242","doi":"https://doi.org/10.37236/9575","mag":"2777599242"},"language":"en","primary_location":{"id":"doi:10.37236/9575","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9575","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v31i3p6/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/v31i3p6/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049237452","display_name":"A. L. Kanunnikov","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andrei L. Kanunnikov","raw_affiliation_strings":["Moscow State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Moscow State University","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083921861","display_name":"V.V. Promyslov","orcid":"https://orcid.org/0000-0003-1525-6458"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Valentin V. Promyslov","raw_affiliation_strings":["Moscow State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Moscow State University","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007117776","display_name":"Ekaterina A. Vassilieva","orcid":null},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210139461","display_name":"Laboratoire d'Informatique de l'\u00c9cole Polytechnique","ror":"https://ror.org/04afed728","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210139461","https://openalex.org/I4210145102","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ekaterina A. Vassilieva","raw_affiliation_strings":["LIX - Laboratoire d'informatique de l'\u00c9cole polytechnique [Palaiseau] (1 Rue Honor\u00e9 d\u2019Estienne d\u2019Orves, B\u00e2timent Alain Turing, 91120 Palaiseau - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIX - Laboratoire d'informatique de l'\u00c9cole polytechnique [Palaiseau] (1 Rue Honor\u00e9 d\u2019Estienne d\u2019Orves, B\u00e2timent Alain Turing, 91120 Palaiseau - France)","institution_ids":["https://openalex.org/I4210139461","https://openalex.org/I142476485"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00101695,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"31","issue":"3","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":1.0,"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":1.0,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/conjecture","display_name":"Conjecture","score":0.7471153736114502},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7385193705558777},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5931403040885925},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.5711182355880737},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.4992392063140869},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.49611958861351013},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.4913887083530426},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.411320298910141},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36804139614105225},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11456236243247986}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7471153736114502},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7385193705558777},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5931403040885925},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.5711182355880737},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4992392063140869},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.49611958861351013},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.4913887083530426},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.411320298910141},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36804139614105225},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11456236243247986},{"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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/9575","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9575","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v31i3p6/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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:1712.08246","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1712.08246","pdf_url":"https://arxiv.org/pdf/1712.08246","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:HAL:hal-04800675v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04800675","pdf_url":"https://hal.science/hal-04800675/document","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":"The Electronic Journal of Combinatorics, 2024, 31, ⟨10.37236/9575⟩","raw_type":"Journal articles"},{"id":"pmh:oai:HAL:hal-03092818v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03092818","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":"2020","raw_type":"Preprints, Working Papers, ..."}],"best_oa_location":{"id":"doi:10.37236/9575","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9575","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v31i3p6/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/F4320319388","display_name":"Moscow Center of Fundamental and Applied Mathematics","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2777599242.pdf"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W627820511","https://openalex.org/W1585244820","https://openalex.org/W1706900508","https://openalex.org/W1806580154","https://openalex.org/W1972550776","https://openalex.org/W1985872741","https://openalex.org/W1999395516","https://openalex.org/W2028897994","https://openalex.org/W2033616652","https://openalex.org/W2036779782","https://openalex.org/W2056514476","https://openalex.org/W2063442271","https://openalex.org/W2070811009","https://openalex.org/W2090024002","https://openalex.org/W2124818311","https://openalex.org/W2134984950","https://openalex.org/W2146486600","https://openalex.org/W2152032738","https://openalex.org/W2298089993","https://openalex.org/W2315362388","https://openalex.org/W2731686496","https://openalex.org/W2952300518","https://openalex.org/W2962832373","https://openalex.org/W2962884658","https://openalex.org/W2964020779","https://openalex.org/W3016629547","https://openalex.org/W3104309820","https://openalex.org/W4230356195"],"related_works":["https://openalex.org/W2964230509","https://openalex.org/W2785232145","https://openalex.org/W1996969552","https://openalex.org/W2165910984","https://openalex.org/W2466298547","https://openalex.org/W4297749837","https://openalex.org/W2037837540","https://openalex.org/W1995202720","https://openalex.org/W4387355916","https://openalex.org/W1667518552"],"abstract_inverted_index":{"Introduced":[0],"by":[1,107],"Goulden":[2],"and":[3,12,37,58,76,85,91,115,160,168,175],"Jackson":[4],"in":[5,45,59,121,177],"their":[6],"1996":[7],"paper,":[8],"the":[9,13,19,30,34,43,46,60,63,69,73,77,82,87,116,138,143,165,169],"matchings-Jack":[10,170],"conjecture":[11,15,167,171],"hypermap-Jack":[14,166],"(also":[16],"known":[17],"as":[18],"b-conjecture)":[20],"are":[21],"two":[22,102],"major":[23],"open":[24],"questions":[25],"relating":[26],"Jack":[27,55,117],"symmetric":[28,35,56,83],"functions,":[29],"representation":[31],"theory":[32],"of":[33,50,62,72,81,89,104,110,130,142,155,158,164],"groups":[36],"combinatorial":[38,131],"maps.":[39],"They":[40,95],"show":[41],"that":[42,100],"coefficients":[44,105,129,159],"power":[47],"sum":[48,53,65],"expansion":[49],"some":[51,98,152,178],"Cauchy":[52],"for":[54],"functions":[57],"logarithm":[61],"same":[64],"interpolate":[66],"respectively":[67],"between":[68,86],"structure":[70],"constants":[71],"class":[74],"algebra":[75,80],"double":[78],"coset":[79],"group":[84],"numbers":[88],"orientable":[90,93],"locally":[92],"hypermaps.":[94],"further":[96],"provide":[97],"evidence":[99],"these":[101],"families":[103,157],"indexed":[106],"three":[108,144],"partitions":[109,145],"a":[111,162],"given":[112],"intege":[113],"$n$":[114],"parameter":[118],"\u03b1are":[119],"polynomials":[120],"$\\beta":[122],"=":[123],"\\alpha":[124],"-1$":[125],"with":[126],"non-negative":[127],"integer":[128],"significance.":[132],"This":[133],"paper":[134],"is":[135,146],"devoted":[136],"to":[137,148],"case":[139],"when":[140],"one":[141],"equal":[147],"$(n)$.":[149],"We":[150],"exhibit":[151],"polynomial":[153],"properties":[154],"both":[156],"prove":[161],"variation":[163],"involving":[172],"labelled":[173],"hypermaps":[174],"matchings":[176],"important":[179],"cases.":[180]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}