{"id":"https://openalex.org/W7204777779","doi":"https://doi.org/10.48550/arxiv.2608.28585","title":"The Tutte polynomial determines the linear coefficient of the Ehrhart polynomial","display_name":"The Tutte polynomial determines the linear coefficient of the Ehrhart polynomial","publication_year":2026,"publication_date":"2026-08-28","ids":{"openalex":"https://openalex.org/W7204777779","doi":"https://doi.org/10.48550/arxiv.2608.28585"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.28585","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28585","pdf_url":"https://arxiv.org/pdf/2608.28585","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/2608.28585","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072534737","display_name":"Erik Panzer","orcid":"https://orcid.org/0000-0002-9897-5812","observed_orcids":["https://orcid.org/0000-0002-9897-5812"]},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Panzer, Erik","raw_affiliation_strings":["Mathematical Institute , University of Oxford , OX2 6GG , UK,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute , University of Oxford , OX2 6GG , UK,","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5072534737"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"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/T10720","display_name":"Complexity and Algorithms in Graphs","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/T10374","display_name":"Advanced Graph Theory Research","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":[{"id":"https://openalex.org/keywords/tutte-polynomial","display_name":"Tutte polynomial","score":0.9599999785423279},{"id":"https://openalex.org/keywords/ehrhart-polynomials","display_name":"Ehrhart polynomials","score":0.9990000128746033},{"id":"https://openalex.org/keywords/linear-coefficients","display_name":"linear coefficients","score":0.9390000104904175},{"id":"https://openalex.org/keywords/matroids","display_name":"matroid theory","score":0.8320000171661377},{"id":"https://openalex.org/keywords/lattice-point-enumeration","display_name":"lattice point enumeration","score":0.5899999737739563}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8277000188827515},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6976000070571899},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.6664000153541565},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6474999785423279},{"id":"https://openalex.org/C14447369","wikidata":"https://www.wikidata.org/wiki/Q7857002","display_name":"Tutte polynomial","level":5,"score":0.5756000280380249},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5559999942779541},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46810001134872437},{"id":"https://openalex.org/C126385604","wikidata":"https://www.wikidata.org/wiki/Q1087609","display_name":"Chromatic polynomial","level":3,"score":0.2815000116825104},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C97395012","wikidata":"https://www.wikidata.org/wiki/Q1422356","display_name":"Reciprocal polynomial","level":4,"score":0.24809999763965607}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.28585","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28585","pdf_url":"https://arxiv.org/pdf/2608.28585","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.28585","doi":"https://doi.org/10.48550/arxiv.2608.28585","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.28585","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.28585","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28585","pdf_url":"https://arxiv.org/pdf/2608.28585","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204777779.pdf","grobid_xml":"https://content.openalex.org/works/W7204777779.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W4480325","https://openalex.org/W2067600800","https://openalex.org/W2068777528","https://openalex.org/W2096833188","https://openalex.org/W2266844767","https://openalex.org/W2788498798","https://openalex.org/W2950275081","https://openalex.org/W2964638337","https://openalex.org/W2973368039","https://openalex.org/W3009362834","https://openalex.org/W3098348313","https://openalex.org/W3161963287","https://openalex.org/W3176295913","https://openalex.org/W3208833106","https://openalex.org/W4313657037","https://openalex.org/W7120181641","https://openalex.org/W7155370092","https://openalex.org/W7162137953"],"related_works":["https://openalex.org/W3105025084","https://openalex.org/W4205169796","https://openalex.org/W4361865425","https://openalex.org/W4414631289","https://openalex.org/W7120181641","https://openalex.org/W3208833106","https://openalex.org/W2991327913","https://openalex.org/W7100860119","https://openalex.org/W3103619716","https://openalex.org/W4405447041"],"abstract_inverted_index":{"We":[0],"prove":[1],"a":[2,29],"formula":[3],"for":[4],"the":[5,9,15,21],"linear":[6],"coefficient":[7],"of":[8,14,31],"Ehrhart":[10,26],"polynomial":[11],"in":[12],"terms":[13],"Tutte":[16],"polynomial.":[17],"Furthermore,":[18],"we":[19],"characterize":[20],"matroids":[22],"that":[23],"extremize":[24],"this":[25],"coefficient,":[27],"proving":[28],"conjecture":[30],"Ferroni.":[32]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-01T00:00:00"}