{"id":"https://openalex.org/W3003528453","doi":"https://doi.org/10.37236/7582","title":"Convexity in Ordered Matroids and the Generalized External Order","display_name":"Convexity in Ordered Matroids and the Generalized External Order","publication_year":2020,"publication_date":"2020-08-21","ids":{"openalex":"https://openalex.org/W3003528453","doi":"https://doi.org/10.37236/7582","mag":"3003528453"},"language":"en","primary_location":{"id":"doi:10.37236/7582","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7582","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p41/pdf","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":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p41/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019995213","display_name":"Bryan R. Gillespie","orcid":"https://orcid.org/0000-0001-8986-7476"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Bryan R. Gillespie","raw_affiliation_strings":["University of California, Berkeley"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Berkeley","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019995213"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.12869458,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"27","issue":"3","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":0.9922000169754028,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9828000068664551,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.9485499858856201},{"id":"https://openalex.org/keywords/oriented-matroid","display_name":"Oriented matroid","score":0.7492943406105042},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7031349539756775},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.674012303352356},{"id":"https://openalex.org/keywords/weighted-matroid","display_name":"Weighted matroid","score":0.6573960185050964},{"id":"https://openalex.org/keywords/tutte-polynomial","display_name":"Tutte polynomial","score":0.5876496434211731},{"id":"https://openalex.org/keywords/graphic-matroid","display_name":"Graphic matroid","score":0.5853444337844849},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.5744388103485107},{"id":"https://openalex.org/keywords/matroid-partitioning","display_name":"Matroid partitioning","score":0.5709612965583801},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5354239344596863},{"id":"https://openalex.org/keywords/distributive-lattice","display_name":"Distributive lattice","score":0.4686027765274048},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.46503323316574097},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4031429588794708},{"id":"https://openalex.org/keywords/distributive-property","display_name":"Distributive property","score":0.33553624153137207},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.30460843443870544},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28497034311294556},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07496723532676697}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.9485499858856201},{"id":"https://openalex.org/C178621168","wikidata":"https://www.wikidata.org/wiki/Q16155113","display_name":"Oriented matroid","level":4,"score":0.7492943406105042},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7031349539756775},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.674012303352356},{"id":"https://openalex.org/C124344645","wikidata":"https://www.wikidata.org/wiki/Q7979897","display_name":"Weighted matroid","level":5,"score":0.6573960185050964},{"id":"https://openalex.org/C14447369","wikidata":"https://www.wikidata.org/wiki/Q7857002","display_name":"Tutte polynomial","level":5,"score":0.5876496434211731},{"id":"https://openalex.org/C111034964","wikidata":"https://www.wikidata.org/wiki/Q5597156","display_name":"Graphic matroid","level":3,"score":0.5853444337844849},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.5744388103485107},{"id":"https://openalex.org/C22425182","wikidata":"https://www.wikidata.org/wiki/Q6787906","display_name":"Matroid partitioning","level":4,"score":0.5709612965583801},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5354239344596863},{"id":"https://openalex.org/C192606457","wikidata":"https://www.wikidata.org/wiki/Q2363730","display_name":"Distributive lattice","level":3,"score":0.4686027765274048},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.46503323316574097},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4031429588794708},{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.33553624153137207},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.30460843443870544},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28497034311294556},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07496723532676697},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.0},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/7582","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7582","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p41/pdf","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:arXiv.org:1712.04080","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1712.04080","pdf_url":"https://arxiv.org/pdf/1712.04080","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":null,"raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/7582","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7582","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p41/pdf","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":0.47999998927116394,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G3604334060","display_name":"Zonotopal algebra and combinatorics","funder_award_id":"1303298","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3003528453.pdf","grobid_xml":"https://content.openalex.org/works/W3003528453.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1553198977","https://openalex.org/W1741136470","https://openalex.org/W1848709520","https://openalex.org/W1912995418","https://openalex.org/W1983739088","https://openalex.org/W1995262757","https://openalex.org/W2008472326","https://openalex.org/W2017373798","https://openalex.org/W2029787168","https://openalex.org/W2031773577","https://openalex.org/W2059323226","https://openalex.org/W2086905250","https://openalex.org/W2131096251","https://openalex.org/W2210453969","https://openalex.org/W2313098266","https://openalex.org/W2405154940","https://openalex.org/W2507648344","https://openalex.org/W2516102042","https://openalex.org/W2903992637","https://openalex.org/W2918466505","https://openalex.org/W2963231815","https://openalex.org/W2963937081","https://openalex.org/W3032496482","https://openalex.org/W3105495689","https://openalex.org/W3141556037","https://openalex.org/W4238651650","https://openalex.org/W4298234358","https://openalex.org/W4391786483","https://openalex.org/W6722858050"],"related_works":["https://openalex.org/W2400862597","https://openalex.org/W1984819493","https://openalex.org/W2378157773","https://openalex.org/W2159059797","https://openalex.org/W2153065381","https://openalex.org/W2980228156","https://openalex.org/W4303709689","https://openalex.org/W2625145881","https://openalex.org/W2763143611","https://openalex.org/W2008472326"],"abstract_inverted_index":{"In":[0,27],"1980,":[1],"Las":[2],"Vergnas":[3],"defined":[4,60],"a":[5,37,51,104,126,131],"notion":[6],"of":[7,20,54,65,72,75,112,125],"discrete":[8],"convexity":[9],"for":[10,56],"oriented":[11],"matroids,":[12],"which":[13,87],"Edelman":[14],"subsequently":[15],"related":[16],"to":[17,35,121],"the":[18,62,83,89,109,118,122,137],"theory":[19],"anti-exchange":[21],"closure":[22],"functions":[23],"and":[24,114],"convex":[25,38,68,73,77],"geometries.":[26],"this":[28,76,99],"paper,":[29],"we":[30,115,129],"use":[31],"generalized":[32,100],"matroid":[33,59,84,94,138],"activity":[34],"construct":[36],"geometry":[39,78],"associated":[40],"with":[41],"an":[42,57,80],"ordered,":[43],"unoriented":[44],"matroid.":[45,127],"The":[46,70],"construction":[47],"in":[48],"particular":[49],"yields":[50],"new":[52,132],"type":[53],"representability":[55,64],"ordered":[58],"by":[61],"affine":[63],"its":[66],"corresponding":[67],"geometry.":[69],"lattice":[71,107,111],"sets":[74,86],"induces":[79],"ordering":[81],"on":[82,93],"independent":[85],"extends":[88],"external":[90,101,123],"active":[91],"order":[92,102,124],"bases.":[95],"We":[96],"show":[97],"that":[98],"forms":[103],"supersolvable":[105],"meet-distributive":[106],"refining":[108],"geometric":[110],"flats,":[113],"uniquely":[116],"characterize":[117],"lattices":[119],"isomorphic":[120],"Finally,":[128],"introduce":[130],"trivariate":[133],"generating":[134],"function":[135],"generalizing":[136],"Tutte":[139],"polynomial.":[140]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
