{"id":"https://openalex.org/W2244693041","doi":"https://doi.org/10.37236/5746","title":"Internally Perfect Matroids","display_name":"Internally Perfect Matroids","publication_year":2017,"publication_date":"2017-06-02","ids":{"openalex":"https://openalex.org/W2244693041","doi":"https://doi.org/10.37236/5746","mag":"2244693041"},"language":"en","primary_location":{"id":"doi:10.37236/5746","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5746","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/10.37236/5746","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090128710","display_name":"Aaron Dall","orcid":"https://orcid.org/0000-0002-4575-3570"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Aaron Dall","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5090128710"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5122,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.5240678,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"24","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":0.9994000196456909,"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":0.9994000196456909,"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":0.9965999722480774,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9962999820709229,"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/matroid","display_name":"Matroid","score":0.9885419607162476},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.797839879989624},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7806288599967957},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6185322403907776},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5624266862869263},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5462758541107178},{"id":"https://openalex.org/keywords/graphic-matroid","display_name":"Graphic matroid","score":0.5319875478744507},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.47269442677497864},{"id":"https://openalex.org/keywords/perfect-power","display_name":"Perfect power","score":0.46336740255355835},{"id":"https://openalex.org/keywords/minor","display_name":"Minor (academic)","score":0.45343154668807983},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4227096438407898},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.41481274366378784},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1481761932373047},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.041578054428100586}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.9885419607162476},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.797839879989624},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7806288599967957},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6185322403907776},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5624266862869263},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5462758541107178},{"id":"https://openalex.org/C111034964","wikidata":"https://www.wikidata.org/wiki/Q5597156","display_name":"Graphic matroid","level":3,"score":0.5319875478744507},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.47269442677497864},{"id":"https://openalex.org/C93446932","wikidata":"https://www.wikidata.org/wiki/Q1972803","display_name":"Perfect power","level":2,"score":0.46336740255355835},{"id":"https://openalex.org/C2779760435","wikidata":"https://www.wikidata.org/wiki/Q5396169","display_name":"Minor (academic)","level":2,"score":0.45343154668807983},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4227096438407898},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.41481274366378784},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1481761932373047},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.041578054428100586},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C15708023","wikidata":"https://www.wikidata.org/wiki/Q80083","display_name":"Humanities","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.37236/5746","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5746","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:recercat.cat:2072/293095","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/108462","pdf_url":null,"source":{"id":"https://openalex.org/S4306402147","display_name":"RECERCAT (Consorci de Serveis Universitaris de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210090028","host_organization_name":"Consorci de Serveis Universitaris de Catalunya","host_organization_lineage":["https://openalex.org/I4210090028"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:upcommons.upc.edu:2117/108462","is_oa":true,"landing_page_url":"https://hdl.handle.net/2117/108462","pdf_url":null,"source":{"id":"https://openalex.org/S4210207057","display_name":"QRU Quaderns de Recerca en Urbanisme","issn_l":"2014-9689","issn":["2014-9689","2385-6777"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310322448","host_organization_name":"Q71272178","host_organization_lineage":["https://openalex.org/P4310322448"],"host_organization_lineage_names":["Q71272178"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:arXiv.org:1510.04532","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1510.04532","pdf_url":"https://arxiv.org/pdf/1510.04532","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":null},{"id":"mag:2244693041","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1510.04532.pdf","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.1510.04532","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1510.04532","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:10.37236/5746","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5746","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":[{"score":0.46000000834465027,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W188858573","https://openalex.org/W1579213680","https://openalex.org/W2218040560","https://openalex.org/W2270392142","https://openalex.org/W2949609089","https://openalex.org/W2951834647"],"related_works":["https://openalex.org/W2963231815","https://openalex.org/W748765031","https://openalex.org/W2030309348","https://openalex.org/W1974783786","https://openalex.org/W2951474039","https://openalex.org/W2170812129","https://openalex.org/W2950164448","https://openalex.org/W2962744969","https://openalex.org/W2033812757","https://openalex.org/W1758887450","https://openalex.org/W2073617714","https://openalex.org/W2951232363","https://openalex.org/W2320008037","https://openalex.org/W2952597554","https://openalex.org/W144967777","https://openalex.org/W772118325","https://openalex.org/W2951444536","https://openalex.org/W2922153215","https://openalex.org/W2607408650","https://openalex.org/W3046868629"],"abstract_inverted_index":{"In":[0,21,47],"1977":[1],"Stanley":[2],"proved":[3],"that":[4,15,70],"the":[5,22,25,41,86],"$h$-vector":[6],"of":[7,27,36,38,61,82,105],"a":[8,18,34,58,98],"matroid":[9,110],"is":[10,17,44,88,111],"an":[11,106],"$\\mathcal{O}$-sequence":[12],"and":[13,76],"conjectured":[14],"it":[16],"pure":[19],"$\\mathcal{O}$-sequence.":[20],"subsequent":[23],"years":[24],"validity":[26],"this":[28,48],"conjecture":[29,87],"has":[30],"been":[31],"shown":[32],"for":[33,84],"variety":[35],"classes":[37,81],"matroids,":[39],"though":[40],"general":[42],"case":[43],"still":[45],"open.":[46],"paper":[49],"we":[50,64],"use":[51],"Las":[52],"Vergnas'":[53],"internal":[54],"order":[55],"to":[56,79,90,97],"introduce":[57],"new":[59],"class":[60],"matroids":[62,72,83],"which":[63,85],"call":[65],"internally":[66,107,112],"perfect.":[67,113],"We":[68,92],"prove":[69,94],"these":[71],"satisfy":[73],"Stanley's":[74],"Conjecture":[75],"compare":[77],"them":[78],"other":[80],"known":[89],"hold.":[91],"also":[93],"that,":[95],"up":[96],"certain":[99],"restriction":[100],"on":[101],"deletions,":[102],"every":[103],"minor":[104],"perfect":[108],"ordered":[109]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}