{"id":"https://openalex.org/W1992906119","doi":"https://doi.org/10.1137/060655596","title":"Rota\u2019s Basis Conjecture for Paving Matroids","display_name":"Rota\u2019s Basis Conjecture for Paving Matroids","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1992906119","doi":"https://doi.org/10.1137/060655596","mag":"1992906119"},"language":"en","primary_location":{"id":"doi:10.1137/060655596","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060655596","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056655545","display_name":"Jim Geelen","orcid":"https://orcid.org/0000-0003-0411-7903"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jim Geelen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5033371311","display_name":"Peter Humphries","orcid":"https://orcid.org/0000-0002-3807-8714"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peter J. Humphries","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056655545"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6741,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.69312403,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"20","issue":"4","first_page":"1042","last_page":"1045"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9976000189781189,"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":0.9976000189781189,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9958000183105469,"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"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9726999998092651,"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":0.9789764881134033},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.8496497869491577},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8072842955589294},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7704973220825195},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7426098585128784},{"id":"https://openalex.org/keywords/statement","display_name":"Statement (logic)","score":0.6616906523704529},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6143512725830078},{"id":"https://openalex.org/keywords/graphic-matroid","display_name":"Graphic matroid","score":0.5460070371627808},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5216786861419678},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47369813919067383},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.46920245885849},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11626800894737244}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.9789764881134033},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.8496497869491577},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8072842955589294},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7704973220825195},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7426098585128784},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.6616906523704529},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6143512725830078},{"id":"https://openalex.org/C111034964","wikidata":"https://www.wikidata.org/wiki/Q5597156","display_name":"Graphic matroid","level":3,"score":0.5460070371627808},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5216786861419678},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47369813919067383},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.46920245885849},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11626800894737244},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/060655596","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060655596","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:CiteSeerX.psu:10.1.1.591.7587","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.591.7587","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uwaterloo.ca/~jfgeelen/publications/RBC.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.63.6806","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.63.6806","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uwaterloo.ca/~jfgeelen/publications/paving.pdf","raw_type":"text"},{"id":"pmh:oai:ir.canterbury.ac.nz:10092/11877","is_oa":false,"landing_page_url":"http://hdl.handle.net/10092/11877","pdf_url":null,"source":{"id":"https://openalex.org/S4306401103","display_name":"University of Canterbury Research Repository (University of Canterbury)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I185492890","host_organization_name":"University of Canterbury","host_organization_lineage":["https://openalex.org/I185492890"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Discussion / Working Papers"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1520990686","https://openalex.org/W1558934860","https://openalex.org/W1988918747","https://openalex.org/W2039481874","https://openalex.org/W2052688974","https://openalex.org/W2082199499","https://openalex.org/W2094412891","https://openalex.org/W2100234888"],"related_works":["https://openalex.org/W4287077747","https://openalex.org/W2088312182","https://openalex.org/W4381492016","https://openalex.org/W1573541561","https://openalex.org/W2949957690","https://openalex.org/W2962978631","https://openalex.org/W2068222471","https://openalex.org/W1964963768","https://openalex.org/W4291556988","https://openalex.org/W2053598067"],"abstract_inverted_index":{"Rota":[0],"conjectured":[1],"that,":[2],"given":[3],"n":[4,14],"disjoint":[5,15],"bases":[6,19,23],"of":[7,17,24,34],"a":[8,28],"rank\u2010n":[9],"matroid":[10],"M,":[11],"there":[12],"are":[13,21],"transversals":[16],"these":[18],"that":[20],"all":[22],"M.":[25],"We":[26],"prove":[27],"stronger":[29],"statement":[30],"for":[31],"the":[32],"class":[33],"paving":[35],"matroids.":[36]},"counts_by_year":[{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
