{"id":"https://openalex.org/W7214092073","doi":"https://doi.org/10.48550/arxiv.2609.25395","title":"On inversion sets of joins in weak Bruhat order","display_name":"On inversion sets of joins in weak Bruhat order","publication_year":2026,"publication_date":"2026-09-21","ids":{"openalex":"https://openalex.org/W7214092073","doi":"https://doi.org/10.48550/arxiv.2609.25395"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.25395","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25395","pdf_url":"https://arxiv.org/pdf/2609.25395","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/2609.25395","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152510804","display_name":"Ming Yean Lim","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lim, Ming Yean","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5152510804"],"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":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/T10849","display_name":"Finite Group Theory Research","score":9.999999747378752e-05,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/weak-bruhat-order","display_name":"weak Bruhat order","score":0.9150000214576721},{"id":"https://openalex.org/keywords/join","display_name":"join","score":0.5789999961853027},{"id":"https://openalex.org/keywords/coxeter-groups","display_name":"Coxeter groups","score":0.8450000286102295},{"id":"https://openalex.org/keywords/meet-semilattices","display_name":"meet-semilattices","score":0.8849999904632568},{"id":"https://openalex.org/keywords/lattices","display_name":"lattices","score":0.781000018119812},{"id":"https://openalex.org/keywords/recursive-algorithm","display_name":"recursive algorithm","score":0.7319999933242798},{"id":"https://openalex.org/keywords/finite-coxeter-groups","display_name":"finite Coxeter groups","score":0.8420000076293945}],"concepts":[{"id":"https://openalex.org/C2778692605","wikidata":"https://www.wikidata.org/wiki/Q4041866","display_name":"Joins","level":2,"score":0.9146000146865845},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.7003999948501587},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6960999965667725},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6628000140190125},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.640999972820282},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5547999739646912},{"id":"https://openalex.org/C143669375","wikidata":"https://www.wikidata.org/wiki/Q7874246","display_name":"Coxeter group","level":2,"score":0.4934999942779541},{"id":"https://openalex.org/C18116961","wikidata":"https://www.wikidata.org/wiki/Q734209","display_name":"Generating set of a group","level":2,"score":0.420199990272522},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3666999936103821},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.3547999858856201},{"id":"https://openalex.org/C2776124973","wikidata":"https://www.wikidata.org/wiki/Q3183033","display_name":"Join (topology)","level":2,"score":0.3544999957084656},{"id":"https://openalex.org/C177274530","wikidata":"https://www.wikidata.org/wiki/Q4978697","display_name":"Bruhat order","level":3,"score":0.35280001163482666},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3497999906539917},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3361000120639801},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.33500000834465027},{"id":"https://openalex.org/C2985459651","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Ordered set","level":2,"score":0.32589998841285706},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C201064014","wikidata":"https://www.wikidata.org/wiki/Q3956993","display_name":"Artin group","level":3,"score":0.2702000141143799},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.267300009727478},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.25360000133514404}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.25395","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25395","pdf_url":"https://arxiv.org/pdf/2609.25395","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.2609.25395","doi":"https://doi.org/10.48550/arxiv.2609.25395","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.25395","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.25395","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25395","pdf_url":"https://arxiv.org/pdf/2609.25395","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/G367387608","display_name":"Parahoric Character Sheaves and Representations of p-Adic Groups","funder_award_id":"2401114","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/W7214092073.pdf","grobid_xml":"https://content.openalex.org/works/W7214092073.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W1901586742","https://openalex.org/W1990751763","https://openalex.org/W2062911855","https://openalex.org/W2065156273","https://openalex.org/W7114803168","https://openalex.org/W7163759507"],"related_works":["https://openalex.org/W1863544524","https://openalex.org/W7163759507","https://openalex.org/W7090844362","https://openalex.org/W1901586742","https://openalex.org/W2964175717","https://openalex.org/W7124146990","https://openalex.org/W7114803168","https://openalex.org/W7055964058","https://openalex.org/W2062911855","https://openalex.org/W2065156273"],"abstract_inverted_index":{"It":[0],"is":[1,8,19,22,83],"well-known":[2],"that":[3,37,81],"any":[4],"Coxeter":[5],"group":[6],"$W$":[7,18,82],"a":[9,23,34,56,65],"meet-semilattice":[10],"with":[11,91],"respect":[12],"to":[13],"weak":[14,41],"order.":[15],"Furthermore,":[16],"when":[17],"finite,":[20],"it":[21],"lattice.":[24],"In":[25,47],"the":[26,48,53,61,70,79],"first":[27],"part":[28],"of":[29,55,58,64,69,72,75],"this":[30],"paper,":[31],"we":[32,51],"give":[33],"recursive":[35],"algorithm":[36],"computes":[38],"joins":[39],"in":[40,67,89],"order":[42],"for":[43],"arbitrary":[44],"finite":[45],"$W$.":[46],"second":[49],"part,":[50],"complete":[52],"proof":[54],"conjecture":[57],"Dyer":[59],"expressing":[60],"inversion":[62,73],"set":[63],"join":[66],"terms":[68],"union":[71],"sets":[74],"each":[76],"factor,":[77],"under":[78],"assumption":[80],"finite.":[84],"Some":[85],"proofs":[86],"were":[87],"developed":[88],"collaboration":[90],"Claude":[92],"Opus":[93],"5.":[94]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-24T00:00:00"}