{"id":"https://openalex.org/W7214907686","doi":"https://doi.org/10.48550/arxiv.2609.37778","title":"Weighted coloop splittings in rank six","display_name":"Weighted coloop splittings in rank six","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214907686","doi":"https://doi.org/10.48550/arxiv.2609.37778"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.37778","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37778","pdf_url":"https://arxiv.org/pdf/2609.37778","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.37778","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068436251","display_name":"James Dylan Douthitt","orcid":"https://orcid.org/0009-0000-5740-1508","observed_orcids":["https://orcid.org/0009-0000-5740-1508"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Douthitt, James Dylan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153553164","display_name":"Lee Kennard","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kennard, Lee","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5066662766","display_name":"Josef Komissar","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Komissar, Josef","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.5131999850273132,"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":0.5131999850273132,"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":0.41920000314712524,"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":0.02539999969303608,"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/regular-matroids","display_name":"regular matroids","score":0.8650000095367432},{"id":"https://openalex.org/keywords/cocircuits","display_name":"cocircuits","score":0.7919999957084656},{"id":"https://openalex.org/keywords/riemannian-geometry","display_name":"Riemannian geometry","score":0.8220000267028809}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.930400013923645},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8474000096321106},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.8184000253677368},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.6912999749183655},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6848000288009644},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.46790000796318054},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4092000126838684},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40400001406669617},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.32120001316070557},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.32089999318122864},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C22425182","wikidata":"https://www.wikidata.org/wiki/Q6787906","display_name":"Matroid partitioning","level":4,"score":0.2669000029563904}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.37778","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37778","pdf_url":"https://arxiv.org/pdf/2609.37778","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},{"id":"doi:10.48550/arxiv.2609.37778","doi":"https://doi.org/10.48550/arxiv.2609.37778","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.37778","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.37778","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37778","pdf_url":"https://arxiv.org/pdf/2609.37778","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3901523274","display_name":"Positive curvature and torus symmetry","funder_award_id":"2402129","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/W7214907686.pdf","grobid_xml":"https://content.openalex.org/works/W7214907686.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W3175258394","https://openalex.org/W4309957496"],"related_works":["https://openalex.org/W4410542857","https://openalex.org/W2040101882","https://openalex.org/W7217241587","https://openalex.org/W7048988341","https://openalex.org/W150214721","https://openalex.org/W2598775073","https://openalex.org/W2570940998","https://openalex.org/W2949938522","https://openalex.org/W2151107742","https://openalex.org/W3005590572"],"abstract_inverted_index":{"With":[0],"a":[1,24,28,39,57,94],"view":[2],"toward":[3],"applications":[4],"in":[5,20,93],"Riemannian":[6,84],"geometry,":[7,85],"we":[8,86],"explore":[9],"coloop":[10],"splitting":[11],"properties":[12],"of":[13,52,75,97],"regular":[14,25,67],"matroids.":[15],"Nienhaus":[16],"showed":[17],"by":[18],"classification":[19],"rank":[21,108,111],"four":[22],"that":[23,88],"matroid":[26,37],"has":[27],"cocircuit":[29],"whose":[30],"deletion":[31],"yields":[32],"two":[33],"coloops":[34],"unless":[35],"the":[36,43,53,89,101],"takes":[38],"particular":[40],"form.":[41],"In":[42],"latter":[44],"case,":[45],"one":[46],"can":[47,104],"split":[48],"off":[49],"any":[50],"element":[51],"ground":[54],"set":[55],"as":[56],"coloop.":[58],"We":[59],"reprove":[60],"this":[61],"using":[62],"Seymour's":[63],"structure":[64],"theorem":[65],"for":[66],"matroids":[68,74],"and":[69,78,100],"prove":[70,87],"an":[71,81],"extension":[72],"to":[73,83,110],"ranks":[76],"five":[77],"six.":[79],"As":[80],"application":[82],"torus":[90],"symmetry":[91],"assumption":[92],"recent":[95],"result":[96],"Mouill\u00e9,":[98],"Nienhaus,":[99],"second":[102],"author":[103],"be":[105],"relaxed":[106],"from":[107],"ten":[109],"nine.":[112]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-01T00:00:00"}