{"id":"https://openalex.org/W2767019843","doi":"https://doi.org/10.37236/7632","title":"Counting Partitions of a Fixed Genus","display_name":"Counting Partitions of a Fixed Genus","publication_year":2018,"publication_date":"2018-11-02","ids":{"openalex":"https://openalex.org/W2767019843","doi":"https://doi.org/10.37236/7632","mag":"2767019843"},"language":"en","primary_location":{"id":"doi:10.37236/7632","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7632","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p26/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":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p26/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040359504","display_name":"Robert Cori","orcid":"https://orcid.org/0000-0001-9776-1196"},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]},{"id":"https://openalex.org/I4210142254","display_name":"Laboratoire Bordelais de Recherche en Informatique","ror":"https://ror.org/03adqg323","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210159245","https://openalex.org/I4210160189"]},{"id":"https://openalex.org/I4210160189","display_name":"Institut Polytechnique de Bordeaux","ror":"https://ror.org/054qv7y42","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Robert Cori","raw_affiliation_strings":["Labri, Universit\u00e9 Bordeaux 1","LaBRI - Universit\u00e9 Bordeaux 1#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Labri, Universit\u00e9 Bordeaux 1","institution_ids":["https://openalex.org/I4210142254"]},{"raw_affiliation_string":"LaBRI - Universit\u00e9 Bordeaux 1#TAB#","institution_ids":["https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210160189"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089863827","display_name":"G\u00e1bor Hetyei","orcid":"https://orcid.org/0000-0003-3596-6289"},"institutions":[{"id":"https://openalex.org/I102149020","display_name":"University of North Carolina at Charlotte","ror":"https://ror.org/04dawnj30","country_code":"US","type":"education","lineage":["https://openalex.org/I102149020"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"G\u00e1bor Hetyei","raw_affiliation_strings":["UNC Charlotte","UNC Charlotte;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UNC Charlotte","institution_ids":["https://openalex.org/I102149020"]},{"raw_affiliation_string":"UNC Charlotte;","institution_ids":["https://openalex.org/I102149020"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09221184,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"25","issue":"4","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":0.9984999895095825,"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":0.9984999895095825,"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/T13506","display_name":"Botanical Research and Chemistry","score":0.982699990272522,"subfield":{"id":"https://openalex.org/subfields/1105","display_name":"Ecology, Evolution, Behavior and Systematics"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9794999957084656,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/genus","display_name":"Genus","score":0.7429438829421997},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.7053939700126648},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5943820476531982},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.49651914834976196},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.4733089208602905},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.45322829484939575},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4409657120704651},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33959659934043884},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2571435868740082},{"id":"https://openalex.org/keywords/zoology","display_name":"Zoology","score":0.11882296204566956},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.07954353094100952}],"concepts":[{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.7429438829421997},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.7053939700126648},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5943820476531982},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49651914834976196},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.4733089208602905},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.45322829484939575},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4409657120704651},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33959659934043884},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2571435868740082},{"id":"https://openalex.org/C90856448","wikidata":"https://www.wikidata.org/wiki/Q431","display_name":"Zoology","level":1,"score":0.11882296204566956},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.07954353094100952},{"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:10.37236/7632","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7632","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p26/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:1710.09992","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.09992","pdf_url":"https://arxiv.org/pdf/1710.09992","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":"mag:2767019843","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1710.09992.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1710.09992","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1710.09992","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.37236/7632","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7632","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p26/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":[{"id":"https://openalex.org/G1142575854","display_name":null,"funder_award_id":"514648","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"},{"id":"https://openalex.org/G762511767","display_name":null,"funder_award_id":"245153","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"}],"funders":[{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2767019843.pdf","grobid_xml":"https://content.openalex.org/works/W2767019843.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W68296891","https://openalex.org/W1579444899","https://openalex.org/W2016084340","https://openalex.org/W2028897994","https://openalex.org/W2034287194","https://openalex.org/W2060521973","https://openalex.org/W2065211664","https://openalex.org/W2143056798","https://openalex.org/W2149293266","https://openalex.org/W2331875213","https://openalex.org/W2340541605"],"related_works":["https://openalex.org/W2963578722","https://openalex.org/W1973404249","https://openalex.org/W1994904485","https://openalex.org/W1989325704","https://openalex.org/W2114443014","https://openalex.org/W2182866687","https://openalex.org/W2580586390","https://openalex.org/W2911903192","https://openalex.org/W1995626171","https://openalex.org/W2243973406","https://openalex.org/W2160659727","https://openalex.org/W2137955495","https://openalex.org/W3116135107","https://openalex.org/W2272235846","https://openalex.org/W2981611891","https://openalex.org/W2079827143","https://openalex.org/W2951487551","https://openalex.org/W1645011610","https://openalex.org/W2949807038","https://openalex.org/W3193253506"],"abstract_inverted_index":{"We":[0,58],"show":[1],"that,":[2],"for":[3,12,67],"any":[4],"fixed":[5],"genus":[6,14,55,68,74],"$g$,":[7],"the":[8,13,47,64],"ordinary":[9],"generating":[10,65],"function":[11,66],"$g$":[15],"partitions":[16,51],"of":[17,49,52],"an":[18],"$n$-element":[19],"set":[20],"into":[21],"$k$":[22],"blocks":[23],"is":[24,56],"algebraic.":[25],"The":[26],"proof":[27],"involves":[28],"showing":[29],"that":[30,46],"each":[31],"such":[32],"partition":[33,44],"may":[34],"be":[35],"reduced":[36],"in":[37],"a":[38,42,53,79],"unique":[39],"way":[40],"to":[41],"primitive":[43,50,76],"and":[45],"number":[48],"given":[54],"finite.":[57],"illustrate":[59],"our":[60],"method":[61],"by":[62],"finding":[63],"$2$":[69,75],"partitions,":[70,77],"after":[71],"identifying":[72],"all":[73],"using":[78],"computer-assisted":[80],"search.":[81]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
