{"id":"https://openalex.org/W3171183718","doi":"https://doi.org/10.1016/j.aam.2022.102410","title":"Ehrhart polynomials of rank two matroids","display_name":"Ehrhart polynomials of rank two matroids","publication_year":2022,"publication_date":"2022-08-03","ids":{"openalex":"https://openalex.org/W3171183718","doi":"https://doi.org/10.1016/j.aam.2022.102410","mag":"3171183718"},"language":"en","primary_location":{"id":"doi:10.1016/j.aam.2022.102410","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.aam.2022.102410","pdf_url":"https://www.sciencedirect.com/science/article/pii/S019688582200094X/pdf","source":{"id":"https://openalex.org/S164906323","display_name":"Advances in Applied Mathematics","issn_l":"0196-8858","issn":["0196-8858","1090-2074"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.sciencedirect.com/science/article/pii/S019688582200094X/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062037243","display_name":"Luis Ferroni","orcid":"https://orcid.org/0000-0001-5181-7932"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Luis Ferroni","raw_affiliation_strings":["Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden"],"raw_orcid":"https://orcid.org/0000-0001-5181-7932","affiliations":[{"raw_affiliation_string":"Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005964308","display_name":"Katharina Jochemko","orcid":"https://orcid.org/0000-0002-0094-6491"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Katharina Jochemko","raw_affiliation_strings":["Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014525588","display_name":"Benjamin Schr\u00f6ter","orcid":"https://orcid.org/0000-0003-3153-5211"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Benjamin Schr\u00f6ter","raw_affiliation_strings":["Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5005964308","https://openalex.org/A5014525588","https://openalex.org/A5062037243"],"corresponding_institution_ids":["https://openalex.org/I86987016"],"apc_list":{"value":2670,"currency":"USD","value_usd":2670},"apc_paid":{"value":2670,"currency":"USD","value_usd":2670},"fwci":4.9007,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.96684685,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"141","issue":null,"first_page":"102410","last_page":"102410"},"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9828000068664551,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9721999764442444,"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/matroid","display_name":"Matroid","score":0.9303892850875854},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9068738222122192},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.7654327154159546},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5935055017471313},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36364269256591797},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2398194968700409}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.9303892850875854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9068738222122192},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.7654327154159546},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5935055017471313},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36364269256591797},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2398194968700409}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1016/j.aam.2022.102410","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.aam.2022.102410","pdf_url":"https://www.sciencedirect.com/science/article/pii/S019688582200094X/pdf","source":{"id":"https://openalex.org/S164906323","display_name":"Advances in Applied Mathematics","issn_l":"0196-8858","issn":["0196-8858","1090-2074"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2106.08183","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.08183","pdf_url":"https://arxiv.org/pdf/2106.08183","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,"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":"pmh:oai:arpi.unipi.it:11568/1326649","is_oa":false,"landing_page_url":"https://hdl.handle.net/11568/1326649","pdf_url":null,"source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"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":"info:eu-repo/semantics/article"},{"id":"pmh:oai:cris.unibo.it:11585/1005131","is_oa":true,"landing_page_url":"https://hdl.handle.net/11585/1005131","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1016/j.aam.2022.102410","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.aam.2022.102410","pdf_url":"https://www.sciencedirect.com/science/article/pii/S019688582200094X/pdf","source":{"id":"https://openalex.org/S164906323","display_name":"Advances in Applied Mathematics","issn_l":"0196-8858","issn":["0196-8858","1090-2074"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1553163256","display_name":null,"funder_award_id":"DP-COFUND-2015","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G2961490949","display_name":null,"funder_award_id":"INdAM-DP-COFUND-2015","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G4166334428","display_name":null,"funder_award_id":"2018-03968","funder_id":"https://openalex.org/F4320316588","funder_display_name":"G\u00f6ran Gustafssons Stiftelser"},{"id":"https://openalex.org/G6680610496","display_name":"Alcoved polytopes - a pathway between geometry and combinatorics","funder_award_id":"2018-03968","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"},{"id":"https://openalex.org/G6951297444","display_name":null,"funder_award_id":"INdAM-DP-COFUND-2015","funder_id":"https://openalex.org/F4320338337","funder_display_name":"H2020 Marie Sk\u0142odowska-Curie Actions"},{"id":"https://openalex.org/G712881263","display_name":null,"funder_award_id":"2018-","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"},{"id":"https://openalex.org/G7464416053","display_name":null,"funder_award_id":"2018-03968","funder_id":"https://openalex.org/F4320322327","funder_display_name":"Knut och Alice Wallenbergs Stiftelse"},{"id":"https://openalex.org/G7907027657","display_name":null,"funder_award_id":"713485","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320316588","display_name":"G\u00f6ran Gustafssons Stiftelser","ror":"https://ror.org/05s5h0e62"},{"id":"https://openalex.org/F4320321908","display_name":"G\u00f6ran Gustafssons Stiftelse f\u00f6r Naturvetenskaplig och Medicinsk Forskning","ror":"https://ror.org/05s5h0e62"},{"id":"https://openalex.org/F4320322327","display_name":"Knut och Alice Wallenbergs Stiftelse","ror":"https://ror.org/004hzzk67"},{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"},{"id":"https://openalex.org/F4320338337","display_name":"H2020 Marie Sk\u0142odowska-Curie Actions","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3171183718.pdf","grobid_xml":"https://content.openalex.org/works/W3171183718.grobid-xml"},"referenced_works_count":58,"referenced_works":["https://openalex.org/W65815112","https://openalex.org/W116212968","https://openalex.org/W318594539","https://openalex.org/W758484163","https://openalex.org/W1411978157","https://openalex.org/W1485110504","https://openalex.org/W1579213680","https://openalex.org/W1595605524","https://openalex.org/W1672638072","https://openalex.org/W1931704346","https://openalex.org/W1987825278","https://openalex.org/W2029948740","https://openalex.org/W2031887950","https://openalex.org/W2042516302","https://openalex.org/W2043992602","https://openalex.org/W2067600800","https://openalex.org/W2068777528","https://openalex.org/W2090366362","https://openalex.org/W2100658172","https://openalex.org/W2117707498","https://openalex.org/W2183446431","https://openalex.org/W2252414431","https://openalex.org/W2329095262","https://openalex.org/W2340149117","https://openalex.org/W2482024337","https://openalex.org/W2487964192","https://openalex.org/W2506766425","https://openalex.org/W2582894873","https://openalex.org/W2763148572","https://openalex.org/W2769741359","https://openalex.org/W2906962023","https://openalex.org/W2914659449","https://openalex.org/W2918466505","https://openalex.org/W2963048153","https://openalex.org/W2963376870","https://openalex.org/W2964127965","https://openalex.org/W2973368039","https://openalex.org/W2988480584","https://openalex.org/W3009362834","https://openalex.org/W3036257878","https://openalex.org/W3098348313","https://openalex.org/W3105025084","https://openalex.org/W3161963287","https://openalex.org/W3176295913","https://openalex.org/W4250083519","https://openalex.org/W4251570596","https://openalex.org/W4254025485","https://openalex.org/W4255288880","https://openalex.org/W4288104457","https://openalex.org/W4300687615","https://openalex.org/W6602649378","https://openalex.org/W6634786645","https://openalex.org/W6677137991","https://openalex.org/W6686083199","https://openalex.org/W6691400022","https://openalex.org/W6745794105","https://openalex.org/W6813918715","https://openalex.org/W6831323537"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2058299944","https://openalex.org/W4233892543","https://openalex.org/W1550144461","https://openalex.org/W4323360720","https://openalex.org/W2783959783","https://openalex.org/W2602164040","https://openalex.org/W2037206237","https://openalex.org/W4310658774","https://openalex.org/W4205300480"],"abstract_inverted_index":{"Over":[0],"a":[1,29,142],"decade":[2],"ago":[3],"De":[4,145],"Loera,":[5,146],"Haws":[6,147],"and":[7,20,95,120,124,148],"K\u00f6ppe":[8],"conjectured":[9],"that":[10,21,68,84,106,131],"Ehrhart":[11,69,91],"polynomials":[12,70,92],"of":[13,24,34,71,73,93,108,111,115,134,144],"matroid":[14,109],"polytopes":[15,110],"have":[16,76,122],"only":[17,78],"positive":[18,79],"coefficients":[19,23],"the":[22,25,44,64,90,101,132,135],"corresponding":[26],"h\u204e-polynomials":[27,107],"form":[28],"unimodal":[30,125],"sequence.":[31],"The":[32],"first":[33,45],"these":[35],"intensively":[36],"studied":[37],"conjectures":[38],"has":[39],"recently":[40],"been":[41],"disproved":[42],"by":[43,66,89,104],"author":[46],"who":[47],"gave":[48],"counterexamples":[49],"in":[50],"all":[51],"ranks":[52],"greater":[53],"than":[54],"or":[55],"equal":[56],"to":[57],"three.":[58],"In":[59,127],"this":[60,129],"article":[61],"we":[62,82],"complete":[63],"picture":[65],"showing":[67],"matroids":[72,114],"lower":[74],"rank":[75,116],"indeed":[77],"coefficients.":[80,126],"Moreover,":[81],"show":[83],"they":[85],"are":[86,118],"coefficient-wise":[87],"bounded":[88],"minimal":[94],"uniform":[96],"matroids.":[97],"We":[98],"furthermore":[99],"address":[100],"second":[102,136],"conjecture":[103],"proving":[105],"sparse":[112],"paving":[113],"two":[117],"real-rooted":[119],"therefore":[121],"log-concave":[123],"particular,":[128],"shows":[130],"h\u204e-polynomial":[133],"hypersimplex":[137],"is":[138],"real-rooted,":[139],"thereby":[140],"strengthening":[141],"result":[143],"K\u00f6ppe.":[149]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}
