{"id":"https://openalex.org/W2341177906","doi":"https://doi.org/10.37236/6130","title":"Top Degree Part in $b$-Conjecture for Unicellular Bipartite Maps","display_name":"Top Degree Part in $b$-Conjecture for Unicellular Bipartite Maps","publication_year":2017,"publication_date":"2017-08-11","ids":{"openalex":"https://openalex.org/W2341177906","doi":"https://doi.org/10.37236/6130","mag":"2341177906"},"language":"en","primary_location":{"id":"doi:10.37236/6130","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6130","pdf_url":null,"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://doi.org/10.37236/6130","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067862225","display_name":"Maciej Do\u0142\u0119ga","orcid":"https://orcid.org/0000-0003-0692-4792"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Maciej Do\u0142\u0119ga","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5067862225"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.78715729,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.77114777,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"24","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":0.9995999932289124,"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":0.9995999932289124,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9973000288009644,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9970999956130981,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.8590141534805298},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8053167462348938},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7468938827514648},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6871320009231567},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5918764472007751},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5320001244544983},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5143369436264038},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5113674998283386},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.49700430035591125},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.451923131942749},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35896992683410645},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.12537920475006104},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09494888782501221},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08596190810203552}],"concepts":[{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.8590141534805298},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8053167462348938},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7468938827514648},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6871320009231567},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5918764472007751},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5320001244544983},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5143369436264038},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5113674998283386},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.49700430035591125},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.451923131942749},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35896992683410645},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.12537920475006104},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09494888782501221},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08596190810203552},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/6130","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6130","pdf_url":null,"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:1604.03288","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1604.03288","pdf_url":"https://arxiv.org/pdf/1604.03288","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:2341177906","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1604.03288","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.1604.03288","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1604.03288","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-journal"}],"best_oa_location":{"id":"doi:10.37236/6130","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6130","pdf_url":null,"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":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W627820511","https://openalex.org/W1656838262","https://openalex.org/W1757536559","https://openalex.org/W1982402793","https://openalex.org/W2021646443","https://openalex.org/W2032246347","https://openalex.org/W2034573815","https://openalex.org/W2050967535","https://openalex.org/W2063442271","https://openalex.org/W2065211664","https://openalex.org/W2090024002","https://openalex.org/W2095362975","https://openalex.org/W2124818311","https://openalex.org/W2160534695","https://openalex.org/W2300707977","https://openalex.org/W2331875213","https://openalex.org/W2488016465","https://openalex.org/W2963065874","https://openalex.org/W3104309820"],"related_works":["https://openalex.org/W2964020779","https://openalex.org/W2030100833","https://openalex.org/W2155491849","https://openalex.org/W2026147416","https://openalex.org/W2164119028","https://openalex.org/W1945954164","https://openalex.org/W2968251710","https://openalex.org/W2913340675","https://openalex.org/W2950386372","https://openalex.org/W3152090362","https://openalex.org/W2952663362","https://openalex.org/W3003584204","https://openalex.org/W2804665354","https://openalex.org/W2892072932","https://openalex.org/W2922736062","https://openalex.org/W2964033488","https://openalex.org/W2741098198","https://openalex.org/W2963356545","https://openalex.org/W2963485559","https://openalex.org/W1925720072"],"abstract_inverted_index":{"Goulden":[0],"and":[1,156,174],"Jackson":[2],"(1996)":[3],"introduced,":[4],"using":[5],"Jack":[6],"symmetric":[7],"functions,":[8],"some":[9,104],"multivariate":[10,85,220],"generating":[11,35,61,86,221],"series":[12,87,222],"$\\psi(\\boldsymbol{x},":[13],"\\boldsymbol{y},\\boldsymbol{z};":[14],"1,":[15],"1+\\beta)$":[16],"with":[17,75,159,170,227,233],"an":[18,99],"additional":[19],"parameter":[20],"$\\beta$":[21,74,97],"that":[22,42,79,102,115,184,215,250],"might":[23],"be":[24,81],"interpreted":[25],"as":[26,83],"a":[27,40,84,138,190,193,202,206],"continuous":[28],"deformation":[29],"of":[30,69,88,96,109,120,129,132,149,196,199,208,211,218,223,241,245,261],"the":[31,50,65,94,107,110,126,130,147,197,216,219,238,242],"rooted":[32],"bipartite":[33,59,91,112,168,225,259],"maps":[34,60,169,212,226,260],"series.":[36,62],"Indeed,":[37],"it":[38,47],"has":[39],"property":[41],"for":[43,124,145,255],"$\\beta":[44,121,142],"\\in":[45],"\\{0,1\\}$,":[46],"specializes":[48],"to":[49,189,192,235],"rooted,":[51,89,166,224,257],"orientable":[52,55,167],"(general,":[53],"i.e.":[54],"or":[56],"not,":[57],"respectively)":[58],"They":[63],"made":[64],"following":[66],"conjecture:":[67],"coefficients":[68,78,131,148,198,244],"$\\psi$":[70,133,150],"are":[71,163],"polynomials":[72],"in":[73,103],"positive":[76],"integer":[77],"can":[80],"written":[82],"general":[90],"maps,":[92],"where":[93],"exponent":[95],"is":[98,134],"integer-valued":[100,209],"statistics":[101,210],"sense":[105],"\"measures":[106],"non-orientability\"":[108],"corresponding":[111],"map.We":[113],"show":[114,183,249],"except":[116],"two":[117,153],"special":[118,140],"values":[119],"=":[122,143],"0,1$":[123],"which":[125,146],"combinatorial":[127],"interpretation":[128],"known,":[135],"there":[136],"exists":[137],"third":[139],"value":[141],"-1$":[144],"indexed":[151],"by":[152,165,179],"partitions":[154],"$\\mu,\\nu$,":[155],"one":[157,161,229],"partition":[158],"only":[160,228],"part":[162,195],"given":[164,178],"arbitrary":[171],"face":[172,230],"degrees":[173,177],"black/white":[175],"vertex":[176],"$\\mu$/$\\nu$,":[180],"respectively.":[181],"We":[182],"this":[185],"evaluation":[186],"corresponds,":[187],"up":[188],"sign,":[191],"top-degree":[194,217],"$\\psi$.":[200,246],"As":[201],"consequence,":[203],"we":[204,248],"introduce":[205],"collection":[207],"$(\\eta)$":[213],"such":[214],"(called":[231],"unicellular)":[232],"respect":[234],"$\\eta$":[236],"gives":[237],"top":[239],"degree":[240],"appropriate":[243],"Finally,":[247],"$b$":[251],"conjecture":[252],"holds":[253],"true":[254],"all":[256],"unicellular":[258],"genus":[262],"at":[263],"most":[264],"$2$.":[265]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2017,"cited_by_count":3}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
