{"id":"https://openalex.org/W7214794573","doi":"https://doi.org/10.48550/arxiv.2609.35550","title":"Nonnegativity of the $g$-polynomial of split matroids","display_name":"Nonnegativity of the $g$-polynomial of split matroids","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214794573","doi":"https://doi.org/10.48550/arxiv.2609.35550"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.35550","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35550","pdf_url":"https://arxiv.org/pdf/2609.35550","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.35550","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022280555","display_name":"Alice L. L. Gao","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gao, Alice L. L.","raw_affiliation_strings":["School of Mathematics and Statistics , Northwestern Polytechnical University , Xi'an , Shaanxi 710072 , P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Northwestern Polytechnical University , Xi'an , Shaanxi 710072 , P.R. China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036069319","display_name":"Matthew H. Y. Xie","orcid":"https://orcid.org/0000-0002-3796-0203","observed_orcids":["https://orcid.org/0000-0002-3796-0203"]},"institutions":[{"id":"https://openalex.org/I136765683","display_name":"Tianjin University of Technology","ror":"https://ror.org/00zbe0w13","country_code":"CN","type":"education","lineage":["https://openalex.org/I136765683"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xie, Matthew H. Y.","raw_affiliation_strings":["School of Mathematical Sciences , Tianjin University of Technology , Tianjin 300384 , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , Tianjin University of Technology , Tianjin 300384 , P. R. China","institution_ids":["https://openalex.org/I136765683"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.9994999766349792,"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":0.9994999766349792,"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/T10374","display_name":"Advanced Graph Theory Research","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.9581000208854675},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8700000047683716},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7961000204086304},{"id":"https://openalex.org/C22425182","wikidata":"https://www.wikidata.org/wiki/Q6787906","display_name":"Matroid partitioning","level":4,"score":0.6407999992370605},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6406000256538391},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6085000038146973},{"id":"https://openalex.org/C111034964","wikidata":"https://www.wikidata.org/wiki/Q5597156","display_name":"Graphic matroid","level":3,"score":0.605400025844574},{"id":"https://openalex.org/C178621168","wikidata":"https://www.wikidata.org/wiki/Q16155113","display_name":"Oriented matroid","level":4,"score":0.5842999815940857},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.4717999994754791},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4528999924659729},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.44670000672340393},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.41499999165534973},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4075999855995178},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4023999869823456},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3393999934196472},{"id":"https://openalex.org/C18116961","wikidata":"https://www.wikidata.org/wiki/Q734209","display_name":"Generating set of a group","level":2,"score":0.29980000853538513},{"id":"https://openalex.org/C124344645","wikidata":"https://www.wikidata.org/wiki/Q7979897","display_name":"Weighted matroid","level":5,"score":0.2718000113964081},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.2524999976158142}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.35550","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35550","pdf_url":"https://arxiv.org/pdf/2609.35550","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.35550","doi":"https://doi.org/10.48550/arxiv.2609.35550","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.35550","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.35550","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35550","pdf_url":"https://arxiv.org/pdf/2609.35550","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G6545402480","display_name":null,"funder_award_id":"12271403","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214794573.pdf","grobid_xml":"https://content.openalex.org/works/W7214794573.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W4405470381","https://openalex.org/W4414973998","https://openalex.org/W4415599726","https://openalex.org/W6910597100","https://openalex.org/W7214611463"],"related_works":["https://openalex.org/W7214611463","https://openalex.org/W4405032077","https://openalex.org/W4311718390","https://openalex.org/W4390114255","https://openalex.org/W6910597100","https://openalex.org/W2144281219","https://openalex.org/W3161963287","https://openalex.org/W2712299146","https://openalex.org/W2095011973","https://openalex.org/W4399554736"],"abstract_inverted_index":{"We":[0,42],"prove":[1],"that":[2,45,90,95],"the":[3,60,65,134,147,177,182,185,189],"$g$-polynomial":[4],"of":[5,79,115,138,150,165,191],"every":[6,46,104],"split":[7,40,50,77,112],"matroid":[8,51,78,113],"has":[9,53],"nonnegative":[10],"coefficients,":[11],"establishing":[12],"Speyer's":[13],"conjecture":[14],"for":[15,57,157,169],"a":[16,32,83,109,126],"class":[17],"closed":[18],"under":[19],"taking":[20],"minors":[21],"and":[22,26,64,99,140,152],"containing":[23],"all":[24,173],"paving":[25],"copaving":[27],"matroids.":[28,171],"Our":[29],"proof":[30,190],"uses":[31],"deletion--contraction":[33],"identity":[34,144,183],"obtained":[35],"by":[36],"constructing":[37],"an":[38,54],"auxiliary":[39],"matroid.":[41],"first":[43],"show":[44],"simple,":[47],"cosimple,":[48],"connected":[49,76,110],"$M$":[52,73],"element":[55],"$e$":[56],"which":[58],"both":[59,96],"deletion":[61],"$M\\setminus":[62,97],"e$":[63,98],"contraction":[66],"$M/e$":[67,100],"are":[68,101],"connected.":[69,102],"More":[70],"generally,":[71],"let":[72],"be":[74],"any":[75],"rank":[80,116],"$k$":[81],"on":[82,118,130,176],"ground":[84],"set":[85],"$E$":[86],"with":[87,155],"$|E|\\ge4$.":[88],"Suppose":[89],"$e\\in":[91],"E$":[92],"is":[93],"such":[94],"For":[103],"$v\\in":[105],"E\\setminus\\{e\\}$,":[106],"we":[107,132],"construct":[108],"elementary":[111],"$N_{e,v}$":[114,139],"$k-1$":[117],"$E\\setminus\\{e,v\\}$":[119],"satisfying":[120],"\\[":[121],"g_M(t)=g_{M\\setminus":[122],"e}(t)+g_{M/e}(t)+t\\,g_{N_{e,v}}(t).":[123],"\\]":[124],"Using":[125],"fixed":[127],"total":[128],"order":[129],"$E$,":[131],"prescribe":[133],"proper":[135],"cyclic":[136],"flats":[137],"their":[141],"ranks.":[142],"The":[143],"follows":[145],"from":[146,162],"covaluative":[148],"formula":[149],"Ferroni":[151],"Schr\u00f6ter":[153],"together":[154],"recurrences":[156],"its":[158],"correction":[159],"polynomials,":[160],"derived":[161],"Ferroni's":[163],"enumeration":[164],"admissible":[166],"Delannoy":[167],"paths":[168],"Schubert":[170],"Since":[172],"three":[174],"matroids":[175],"right":[178],"have":[179],"fewer":[180],"elements,":[181],"supplies":[184],"induction":[186],"step":[187],"in":[188],"nonnegativity.":[192]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}