{"id":"https://openalex.org/W2593838753","doi":"https://doi.org/10.1137/140972421","title":"Matroids Representable Over Fields With a Common Subfield","display_name":"Matroids Representable Over Fields With a Common Subfield","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2593838753","doi":"https://doi.org/10.1137/140972421","mag":"2593838753"},"language":"en","primary_location":{"id":"doi:10.1137/140972421","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140972421","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1401.7040","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040504830","display_name":"Peter Nelson","orcid":"https://orcid.org/0000-0003-4108-635X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peter Nelson","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5046528024","display_name":"Stefan H. M. van Zwam","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stefan H. M. van Zwam","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3634,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.7043956,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"29","issue":"2","first_page":"796","last_page":"810"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9976999759674072,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9976999759674072,"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/T11130","display_name":"Coding theory and cryptography","score":0.9758999943733215,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9574000239372253,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.980292558670044},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6708673238754272},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6480240225791931},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.6134482622146606},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5312017798423767},{"id":"https://openalex.org/keywords/graphic-matroid","display_name":"Graphic matroid","score":0.5100436806678772},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4826798737049103},{"id":"https://openalex.org/keywords/projective-plane","display_name":"Projective plane","score":0.45200955867767334},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44195452332496643},{"id":"https://openalex.org/keywords/minor","display_name":"Minor (academic)","score":0.41112104058265686},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1876271367073059},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16526436805725098},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09419387578964233}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.980292558670044},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6708673238754272},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6480240225791931},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.6134482622146606},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5312017798423767},{"id":"https://openalex.org/C111034964","wikidata":"https://www.wikidata.org/wiki/Q5597156","display_name":"Graphic matroid","level":3,"score":0.5100436806678772},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4826798737049103},{"id":"https://openalex.org/C39290043","wikidata":"https://www.wikidata.org/wiki/Q1475760","display_name":"Projective plane","level":3,"score":0.45200955867767334},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44195452332496643},{"id":"https://openalex.org/C2779760435","wikidata":"https://www.wikidata.org/wiki/Q5396169","display_name":"Minor (academic)","level":2,"score":0.41112104058265686},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1876271367073059},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16526436805725098},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09419387578964233},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/140972421","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140972421","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1401.7040","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1401.7040","pdf_url":"https://arxiv.org/pdf/1401.7040","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:2593838753","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1401.7040.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":"pmh:oai:CiteSeerX.psu:10.1.1.756.1953","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.756.1953","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1401.7040.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1401.7040","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1401.7040","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1401.7040","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1401.7040","pdf_url":"https://arxiv.org/pdf/1401.7040","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8851393816","display_name":null,"funder_award_id":"1161650","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W2008773627","https://openalex.org/W2047871605","https://openalex.org/W2068049130","https://openalex.org/W2090551951","https://openalex.org/W2102115128","https://openalex.org/W2138481685"],"related_works":["https://openalex.org/W2964212704","https://openalex.org/W2804496107","https://openalex.org/W2949237857","https://openalex.org/W3010584070","https://openalex.org/W2049444126","https://openalex.org/W1997357497","https://openalex.org/W2049478732","https://openalex.org/W2047779705","https://openalex.org/W2949419637","https://openalex.org/W1993934378","https://openalex.org/W3100204681","https://openalex.org/W2069962574","https://openalex.org/W3101145497","https://openalex.org/W1993456560","https://openalex.org/W2275781839","https://openalex.org/W2005661925","https://openalex.org/W3099644352","https://openalex.org/W2019538680","https://openalex.org/W2780241915","https://openalex.org/W2754893346"],"abstract_inverted_index":{"A":[0],"matroid":[1],"is":[2,6,37],"GF$(q)$-regular":[3],"if":[4],"it":[5],"representable":[7],"over":[8,28,41],"all":[9,64],"proper":[10],"superfields":[11],"of":[12,35,58,63],"the":[13,33],"field":[14],"GF$(q)$.":[15],"We":[16,53],"show":[17],"that,":[18],"for":[19,46],"highly":[20],"connected":[21],"matroids":[22],"having":[23],"a":[24,31],"large":[25],"projective":[26],"geometry":[27],"GF$(q)$":[29],"as":[30],"minor,":[32],"property":[34],"GF$(q)$-regularity":[36],"equivalent":[38],"to":[39],"representability":[40],"both":[42],"GF$(q^2)$":[43],"and":[44],"GF$(q^t)$":[45],"some":[47],"odd":[48],"integer":[49],"$t":[50],"\\ge":[51],"3$.":[52],"do":[54],"this":[55],"by":[56],"means":[57],"an":[59],"exact":[60],"structural":[61],"description":[62],"such":[65],"matroids.":[66]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}