{"id":"https://openalex.org/W1645694748","doi":"https://doi.org/10.37236/3226","title":"Direct Bijective Computation of the Generating Series for 2 and 3-Connection Coefficients of the Symmetric Group","display_name":"Direct Bijective Computation of the Generating Series for 2 and 3-Connection Coefficients of the Symmetric Group","publication_year":2013,"publication_date":"2013-04-09","ids":{"openalex":"https://openalex.org/W1645694748","doi":"https://doi.org/10.37236/3226","mag":"1645694748"},"language":"en","primary_location":{"id":"doi:10.37236/3226","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3226","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p6/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":"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/v20i2p6/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089720550","display_name":"Alejandro H. Morales","orcid":"https://orcid.org/0000-0002-2848-3230"},"institutions":[{"id":"https://openalex.org/I159129438","display_name":"Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al","ror":"https://ror.org/002rjbv21","country_code":"CA","type":"education","lineage":["https://openalex.org/I159129438","https://openalex.org/I49663120"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Alejandro H. Morales","raw_affiliation_strings":["Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al","Universite du Quebec `a Montreal"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al","institution_ids":["https://openalex.org/I159129438"]},{"raw_affiliation_string":"Universite du Quebec `a Montreal","institution_ids":["https://openalex.org/I159129438"]}]},{"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"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ekaterina A. Vassilieva","raw_affiliation_strings":["Ecole Polytechnique, Palaiseau","Ecole Polytechnique, Palaiseau,"],"affiliations":[{"raw_affiliation_string":"Ecole Polytechnique, Palaiseau","institution_ids":[]},{"raw_affiliation_string":"Ecole Polytechnique, Palaiseau,","institution_ids":["https://openalex.org/I142476485"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089720550"],"corresponding_institution_ids":["https://openalex.org/I159129438"],"apc_list":null,"apc_paid":null,"fwci":0.5636,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.59095831,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"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":0.9998999834060669,"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":0.9998999834060669,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.9654299020767212},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7738924026489258},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.645823061466217},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.6384890675544739},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.6222472786903381},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6141856908798218},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5740165710449219},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.570720374584198},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.46649739146232605},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.45495831966400146},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.43106958270072937},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.41291895508766174},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37947046756744385},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37664955854415894},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32511723041534424},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1222836971282959},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11870986223220825}],"concepts":[{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.9654299020767212},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7738924026489258},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.645823061466217},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.6384890675544739},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.6222472786903381},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6141856908798218},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5740165710449219},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.570720374584198},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.46649739146232605},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.45495831966400146},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.43106958270072937},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.41291895508766174},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37947046756744385},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37664955854415894},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32511723041534424},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1222836971282959},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11870986223220825},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/3226","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3226","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p6/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:1101.3614","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1101.3614","pdf_url":"https://arxiv.org/pdf/1101.3614","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":null,"raw_type":"text"},{"id":"mag:1645694748","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1101.3614","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.1101.3614","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1101.3614","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:10.37236/3226","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3226","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p6/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":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1645694748.pdf","grobid_xml":"https://content.openalex.org/works/W1645694748.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1579213680","https://openalex.org/W1585244820","https://openalex.org/W1985872741","https://openalex.org/W1999395516","https://openalex.org/W1999660929","https://openalex.org/W2028897994","https://openalex.org/W2034573815","https://openalex.org/W2041751801","https://openalex.org/W2056514476","https://openalex.org/W2066309197","https://openalex.org/W2096474673","https://openalex.org/W2103292908","https://openalex.org/W2146486600","https://openalex.org/W2300515062","https://openalex.org/W2315362388","https://openalex.org/W2593478009","https://openalex.org/W2602973343","https://openalex.org/W2952041851"],"related_works":["https://openalex.org/W2962884658","https://openalex.org/W2949126658","https://openalex.org/W2731686496","https://openalex.org/W2070811009","https://openalex.org/W2963188278","https://openalex.org/W2466298547","https://openalex.org/W2301508594","https://openalex.org/W3162327646","https://openalex.org/W2264367474","https://openalex.org/W2951124145","https://openalex.org/W2999405026","https://openalex.org/W2599653818","https://openalex.org/W2090056566","https://openalex.org/W2297416283","https://openalex.org/W2794799741","https://openalex.org/W2048226952","https://openalex.org/W585808440","https://openalex.org/W2054586673","https://openalex.org/W2042922791","https://openalex.org/W2561230339"],"abstract_inverted_index":{"We":[0],"evaluate":[1],"combinatorially":[2],"certain":[3],"connection":[4],"coefficients":[5,45,63],"of":[6,14,16,23,35,43,54,61,81,92,120],"the":[7,12,55,79,93,103,129,133],"symmetric":[8,56],"group":[9],"that":[10,77],"count":[11],"number":[13],"factorizations":[15,27,119],"a":[17,21,74,106,121],"long":[18,122],"cycle":[19,123],"as":[20],"product":[22],"three":[24],"permutations.":[25],"Such":[26],"admit":[28],"an":[29,87],"important":[30],"topological":[31],"interpretation":[32],"in":[33,102],"terms":[34],"unicellular":[36],"constellations":[37],"on":[38],"orientable":[39],"surfaces.":[40],"Algebraic":[41],"computation":[42],"these":[44,62,97],"was":[46],"first":[47],"done":[48],"by":[49],"Jackson":[50],"using":[51],"irreducible":[52],"characters":[53],"group.":[57],"However,":[58],"bijective":[59],"computations":[60],"are":[64],"so":[65],"far":[66],"limited":[67],"to":[68,73,112,118],"very":[69],"special":[70],"cases.":[71],"Thanks":[72],"new":[75],"bijection":[76,104,117],"refines":[78],"work":[80],"Schaeffer":[82],"and":[83],"Vassilieva,":[84],"we":[85,127],"give":[86],"explicit":[88],"closed":[89],"form":[90],"evaluation":[91],"generating":[94,135],"series":[95],"for":[96,132],"coefficients.":[98],"The":[99],"main":[100],"ingredient":[101],"is":[105],"modified":[107],"oriented":[108],"tricolored":[109],"tree":[110],"tractable":[111],"enumerate.":[113],"Finally,":[114],"reducing":[115],"this":[116],"into":[124],"two":[125],"permutations,":[126],"get":[128],"analogue":[130],"formula":[131],"corresponding":[134],"series.":[136]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-15T08:11:43.952461","created_date":"2025-10-10T00:00:00"}
