{"id":"https://openalex.org/W2006004129","doi":"https://doi.org/10.1137/13091837x","title":"Intertwining Connectivities in Representable Matroids","display_name":"Intertwining Connectivities in Representable Matroids","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2006004129","doi":"https://doi.org/10.1137/13091837x","mag":"2006004129"},"language":"en","primary_location":{"id":"doi:10.1137/13091837x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/13091837x","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/1304.6488","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007554852","display_name":"Tony Huynh","orcid":"https://orcid.org/0000-0002-6908-923X"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Tony Huynh","raw_affiliation_strings":["Sapienza Universita di Roma (University of Rome)"],"affiliations":[{"raw_affiliation_string":"Sapienza Universita di Roma (University of Rome)","institution_ids":["https://openalex.org/I861853513"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090328279","display_name":"Stefan van Zwam","orcid":null},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stefan H. M. van Zwam","raw_affiliation_strings":["Princeton University#TAB#"],"affiliations":[{"raw_affiliation_string":"Princeton University#TAB#","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5007554852"],"corresponding_institution_ids":["https://openalex.org/I861853513"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08066755,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"1","first_page":"188","last_page":"196"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9997000098228455,"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/T12288","display_name":"Optimization and Search Problems","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9905968904495239},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.621417760848999},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5856286883354187},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5741370916366577},{"id":"https://openalex.org/keywords/minor","display_name":"Minor (academic)","score":0.5329628586769104},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5042058229446411},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.49985456466674805},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.47270748019218445},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3974228501319885},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2734989523887634},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18033066391944885},{"id":"https://openalex.org/keywords/humanities","display_name":"Humanities","score":0.05007252097129822},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.041181325912475586},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.03606057167053223}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.9905968904495239},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.621417760848999},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5856286883354187},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5741370916366577},{"id":"https://openalex.org/C2779760435","wikidata":"https://www.wikidata.org/wiki/Q5396169","display_name":"Minor (academic)","level":2,"score":0.5329628586769104},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5042058229446411},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.49985456466674805},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.47270748019218445},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3974228501319885},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2734989523887634},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18033066391944885},{"id":"https://openalex.org/C15708023","wikidata":"https://www.wikidata.org/wiki/Q80083","display_name":"Humanities","level":1,"score":0.05007252097129822},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.041181325912475586},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.03606057167053223},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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":7,"locations":[{"id":"doi:10.1137/13091837x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/13091837x","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:1304.6488","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1304.6488","pdf_url":"https://arxiv.org/pdf/1304.6488","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:2006004129","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1304.6488v1","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:cwi:oai:cwi.nl:23468","is_oa":true,"landing_page_url":"https://ir.cwi.nl/pub/23468","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"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":"SIAM Journal on Discrete Mathematics, 28(1), 188 - 196","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.769.477","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.769.477","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/1304.6488.pdf","raw_type":"text"},{"id":"pmh:oai:dipot.ulb.ac.be:2013/264102","is_oa":true,"landing_page_url":"http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/264102","pdf_url":null,"source":{"id":"https://openalex.org/S4306401063","display_name":"D\u00e9p\u00f4t institutionnel de l'Universit\u00e9 libre de Bruxelles (Universit\u00e9 Libre de Bruxelles)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I132053463","host_organization_name":"Universit\u00e9 Libre de Bruxelles","host_organization_lineage":["https://openalex.org/I132053463"],"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":"SIAM journal on discrete mathematics","raw_type":"info:ulb-repo/semantics/openurl/article"},{"id":"doi:10.48550/arxiv.1304.6488","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1304.6488","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:1304.6488","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1304.6488","pdf_url":"https://arxiv.org/pdf/1304.6488","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/G5365867299","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G6507447573","display_name":null,"funder_award_id":"several","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"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"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1506349347","https://openalex.org/W1967459533","https://openalex.org/W1972514464","https://openalex.org/W1981907670","https://openalex.org/W1999177816","https://openalex.org/W2006587062","https://openalex.org/W2012160996","https://openalex.org/W2022523090","https://openalex.org/W2067016370","https://openalex.org/W2068183348","https://openalex.org/W2158421820","https://openalex.org/W2161005000","https://openalex.org/W2162113336","https://openalex.org/W2329866321","https://openalex.org/W2949419637"],"related_works":["https://openalex.org/W2161624735","https://openalex.org/W2068855533","https://openalex.org/W2522278172","https://openalex.org/W2962812419","https://openalex.org/W2020663493","https://openalex.org/W3134016517","https://openalex.org/W2083479207","https://openalex.org/W2084164749","https://openalex.org/W2023071135","https://openalex.org/W1975106431","https://openalex.org/W3100613408","https://openalex.org/W2158849792","https://openalex.org/W2951978258","https://openalex.org/W2331971360","https://openalex.org/W2967438270","https://openalex.org/W35507583","https://openalex.org/W2081769494","https://openalex.org/W2548335339","https://openalex.org/W2811224401","https://openalex.org/W2321266876"],"abstract_inverted_index":{"Let":[0],"$M$":[1,45,96],"be":[2],"a":[3,72,77,90,93],"representable":[4,70],"matroid":[5],"and":[6,29,62,92],"$Q,":[7],"R,":[8],"S,":[9],"T$":[10],"subsets":[11],"of":[12,59,95],"the":[13,18,30],"ground":[14],"set":[15],"such":[16,55,87],"that":[17,21,33,43,56,82,88],"smallest":[19,31],"separation":[20,32],"separates":[22,34],"$Q$":[23],"from":[24,36],"$R$":[25],"has":[26,38],"order":[27,39],"$k$,":[28],"$S$":[35],"$T$":[37],"$l$.":[40],"We":[41],"prove":[42,76],"if":[44],"is":[46,51,102],"sufficiently":[47],"large,":[48],"then":[49],"there":[50],"an":[52],"element":[53],"$e$":[54,86],"in":[57],"one":[58],"$M\\backslash":[60],"e$":[61],"$M\\!/e$":[63],"both":[64,89],"connectivities":[65],"are":[66,97],"preserved.":[67,98],"For":[68],"matroids":[69],"over":[71],"finite":[73],"field":[74],"we":[75,80,83],"stronger":[78],"result:":[79],"show":[81],"can":[84],"remove":[85],"connectivity":[91],"minor":[94],"(A":[99],"corrected":[100],"version":[101],"attached.)":[103]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}