{"id":"https://openalex.org/W3129190938","doi":"https://doi.org/10.1007/s00493-023-00062-3","title":"Sweeps, Polytopes, Oriented Matroids, and Allowable Graphs of Permutations","display_name":"Sweeps, Polytopes, Oriented Matroids, and Allowable Graphs of Permutations","publication_year":2023,"publication_date":"2023-10-23","ids":{"openalex":"https://openalex.org/W3129190938","doi":"https://doi.org/10.1007/s00493-023-00062-3","mag":"3129190938"},"language":"en","primary_location":{"id":"doi:10.1007/s00493-023-00062-3","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00493-023-00062-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-023-00062-3.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00493-023-00062-3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039314003","display_name":"Arnau Padrol","orcid":"https://orcid.org/0000-0003-4747-2729"},"institutions":[{"id":"https://openalex.org/I71999127","display_name":"Universitat de Barcelona","ror":"https://ror.org/021018s57","country_code":"ES","type":"education","lineage":["https://openalex.org/I71999127"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Arnau Padrol","raw_affiliation_strings":["Departament de Matem\u00e0tiques i Inform\u00e0tica, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007, Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques i Inform\u00e0tica, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007, Barcelona, Spain","institution_ids":["https://openalex.org/I71999127"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058901817","display_name":"Eva Philippe","orcid":"https://orcid.org/0000-0001-6802-0970"},"institutions":[{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Eva Philippe","raw_affiliation_strings":["Sorbonne Universit\u00e9 and Universit\u00e9 de Paris, CNRS, IMJ-PRG, 75005, Paris, France"],"affiliations":[{"raw_affiliation_string":"Sorbonne Universit\u00e9 and Universit\u00e9 de Paris, CNRS, IMJ-PRG, 75005, Paris, France","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5039314003"],"corresponding_institution_ids":["https://openalex.org/I71999127"],"apc_list":null,"apc_paid":null,"fwci":2.0234,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.80260087,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"44","issue":"1","first_page":"63","last_page":"123"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":1.0,"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":1.0,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9865999817848206,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9858999848365784,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.922693133354187},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.8291410207748413},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7809836864471436},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7459632158279419},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.4805227220058441},{"id":"https://openalex.org/keywords/graphic-matroid","display_name":"Graphic matroid","score":0.47574353218078613},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.45072272419929504},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.4466955363750458},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4358220398426056},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4313593804836273},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3988465368747711},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13599854707717896}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.922693133354187},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.8291410207748413},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7809836864471436},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7459632158279419},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.4805227220058441},{"id":"https://openalex.org/C111034964","wikidata":"https://www.wikidata.org/wiki/Q5597156","display_name":"Graphic matroid","level":3,"score":0.47574353218078613},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.45072272419929504},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.4466955363750458},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4358220398426056},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4313593804836273},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3988465368747711},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13599854707717896},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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":3,"locations":[{"id":"doi:10.1007/s00493-023-00062-3","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00493-023-00062-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-023-00062-3.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2102.06134","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2102.06134","pdf_url":"https://arxiv.org/pdf/2102.06134","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-04460337v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04460337","pdf_url":"https://hal.science/hal-04460337/document","source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Combinatorica, 2023, ⟨10.1007/s00493-023-00062-3⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.1007/s00493-023-00062-3","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00493-023-00062-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-023-00062-3.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1320060331","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/50110001103","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G1598597440","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/5011000110","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G1643949827","display_name":null,"funder_award_id":"AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G2262748287","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G2447788411","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G2810595902","display_name":null,"funder_award_id":"PID2019-106188GB-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G2969783435","display_name":null,"funder_award_id":"CIN/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3008140224","display_name":null,"funder_award_id":"I 5788","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G300979063","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3219925899","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3480869486","display_name":null,"funder_award_id":"13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G4126322094","display_name":null,"funder_award_id":"01100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G4983240618","display_name":null,"funder_award_id":"ANR-17-CE40-0018","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5009866625","display_name":null,"funder_award_id":"ANR-17-CE40-0018","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G5080475149","display_name":null,"funder_award_id":"10.13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G661330594","display_name":null,"funder_award_id":"00110","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G6685425346","display_name":null,"funder_award_id":"0011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G6803667113","display_name":null,"funder_award_id":"ANR-17","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7084143925","display_name":null,"funder_award_id":"AEI/10","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7264301175","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7266728691","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G731785543","display_name":null,"funder_award_id":"21.SI03.64658","funder_id":"https://openalex.org/F4320312331","funder_display_name":"Banco Santander"},{"id":"https://openalex.org/G7535663061","display_name":null,"funder_award_id":"AEI/10.","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G8260616629","display_name":null,"funder_award_id":"011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G8517791338","display_name":null,"funder_award_id":"MCIN/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320323808","funder_display_name":"Universidad de Cantabria"},{"id":"https://openalex.org/G8638682022","display_name":null,"funder_award_id":"10.13039/50110001103","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G8684520763","display_name":null,"funder_award_id":"PID2019","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320312331","display_name":"Banco Santander","ror":"https://ror.org/017d1hs72"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320323428","display_name":"Universitat de Barcelona","ror":"https://ror.org/021018s57"},{"id":"https://openalex.org/F4320323808","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3129190938.pdf"},"referenced_works_count":84,"referenced_works":["https://openalex.org/W81443782","https://openalex.org/W94985437","https://openalex.org/W109851977","https://openalex.org/W1512237513","https://openalex.org/W1546959834","https://openalex.org/W1554645347","https://openalex.org/W1592859567","https://openalex.org/W1978221169","https://openalex.org/W1981402876","https://openalex.org/W1985065217","https://openalex.org/W1986181473","https://openalex.org/W1995154714","https://openalex.org/W1997625405","https://openalex.org/W1998563847","https://openalex.org/W2001367217","https://openalex.org/W2003775453","https://openalex.org/W2004358658","https://openalex.org/W2010608365","https://openalex.org/W2014471682","https://openalex.org/W2017724411","https://openalex.org/W2020328701","https://openalex.org/W2028416480","https://openalex.org/W2029269420","https://openalex.org/W2029428693","https://openalex.org/W2030435702","https://openalex.org/W2035440108","https://openalex.org/W2041286995","https://openalex.org/W2047309836","https://openalex.org/W2049262740","https://openalex.org/W2050230854","https://openalex.org/W2051998168","https://openalex.org/W2053598067","https://openalex.org/W2066789110","https://openalex.org/W2067320522","https://openalex.org/W2072767456","https://openalex.org/W2074065886","https://openalex.org/W2074378119","https://openalex.org/W2079723511","https://openalex.org/W2085821474","https://openalex.org/W2086297027","https://openalex.org/W2089773861","https://openalex.org/W2094018674","https://openalex.org/W2094576395","https://openalex.org/W2107382982","https://openalex.org/W2109178998","https://openalex.org/W2110451458","https://openalex.org/W2120934134","https://openalex.org/W2130848020","https://openalex.org/W2148791034","https://openalex.org/W2160283861","https://openalex.org/W2167816765","https://openalex.org/W2168397817","https://openalex.org/W2258519372","https://openalex.org/W2345680079","https://openalex.org/W2404367485","https://openalex.org/W2405154940","https://openalex.org/W2498084162","https://openalex.org/W2504355181","https://openalex.org/W2583429401","https://openalex.org/W2784325552","https://openalex.org/W2786360563","https://openalex.org/W2951517720","https://openalex.org/W2962840653","https://openalex.org/W2962867705","https://openalex.org/W2971330320","https://openalex.org/W2972207996","https://openalex.org/W3020876960","https://openalex.org/W3121911326","https://openalex.org/W3163227630","https://openalex.org/W3164802612","https://openalex.org/W4205460512","https://openalex.org/W4206570602","https://openalex.org/W4212906638","https://openalex.org/W4213074663","https://openalex.org/W4214853624","https://openalex.org/W4229982091","https://openalex.org/W4234371219","https://openalex.org/W4242614704","https://openalex.org/W4246108584","https://openalex.org/W4250468486","https://openalex.org/W4251391716","https://openalex.org/W4254205555","https://openalex.org/W4385807544","https://openalex.org/W6628756614"],"related_works":["https://openalex.org/W1988375385","https://openalex.org/W2058489697","https://openalex.org/W2271998444","https://openalex.org/W2368666440","https://openalex.org/W2379298228","https://openalex.org/W2365825493","https://openalex.org/W1019084690","https://openalex.org/W2135545610","https://openalex.org/W2365741713","https://openalex.org/W1608104040"],"abstract_inverted_index":{"Abstract":[0],"A":[1,214],"sweep":[2,65,71,79,95,115,167,188,239],"of":[3,17,19,34,37,46,48,53,62,75,85,98,103,133,157,178,181,187,198,205,220,224,235],"a":[4,13,54,131,171,175,185,202],"point":[5,21,55],"configuration":[6,56],"is":[7,140,174],"any":[8],"ordered":[9],"partition":[10],"induced":[11],"by":[12,27,228],"linear":[14],"functional.":[15],"Posets":[16],"sweeps":[18,47,134],"planar":[20],"configurations":[22],"were":[23],"formalized":[24],"and":[25,29,101,118,122,146,200,237],"abstracted":[26],"Goodman":[28],"Pollack":[30],"under":[31],"the":[32,68,86,94,137,179,206,233],"theory":[33],"allowable":[35,218,229],"sequences":[36,91],"permutations.":[38],"We":[39,110,160],"introduce":[40],"two":[41],"generalizations":[42],"that":[43,70,147,162,173],"model":[44],"posets":[45],"higher":[49,108],"dimensional":[50],"configurations.":[51],"Sweeps":[52],"are":[57,73,92,130,217],"in":[58,135,155],"bijection":[59],"with":[60],"faces":[61],"an":[63],"associated":[64],"polytope.":[66],"Mimicking":[67],"fact":[69],"polytopes":[72,189,197],"projections":[74],"permutahedra,":[76],"we":[77],"define":[78],"oriented":[80,88,96,116,153,165,168,240],"matroids":[81,97,117,154,169],"as":[82,194],"strong":[83,112,207],"maps":[84],"braid":[87],"matroid.":[89],"Allowable":[90],"then":[93],"rank":[99],"2,":[100],"many":[102],"their":[104],"properties":[105],"extend":[106],"to":[107,142,151],"rank.":[109],"show":[111],"ties":[113],"between":[114],"both":[119],"modular":[120],"hyperplanes":[121],"Dilworth":[123],"truncations":[124],"from":[125],"(unoriented)":[126],"matroid":[127],"theory.":[128],"Pseudo-sweeps":[129],"generalization":[132,216],"which":[136],"sweeping":[138],"hyperplane":[139],"allowed":[141],"slightly":[143],"change":[144],"direction,":[145],"can":[148,191],"be":[149,192],"extended":[150],"arbitrary":[152],"terms":[156],"cellular":[158,212],"strings.":[159,213],"prove":[161],"for":[163,211],"sweepable":[164],"matroids,":[166],"provide":[170],"sphere":[172],"deformation":[176],"retract":[177],"poset":[180],"pseudo-sweeps.":[182],"This":[183],"generalizes":[184],"property":[186],"(which":[190],"interpreted":[193],"monotone":[195],"path":[196],"zonotopes),":[199],"solves":[201],"special":[203],"case":[204],"Generalized":[208],"Baues":[209],"Problem":[210],"second":[215],"graphs":[219],"permutations:":[221],"symmetric":[222],"sets":[223],"permutations":[225],"pairwise":[226],"connected":[227],"sequences.":[230],"They":[231],"have":[232],"structure":[234],"acycloids":[236],"include":[238],"matroids.":[241]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}