{"id":"https://openalex.org/W1560563637","doi":"https://doi.org/10.37236/1143","title":"Chains, Subwords, and Fillings: Strong Equivalence of Three Definitions of the Bruhat Order","display_name":"Chains, Subwords, and Fillings: Strong Equivalence of Three Definitions of the Bruhat Order","publication_year":2006,"publication_date":"2006-03-07","ids":{"openalex":"https://openalex.org/W1560563637","doi":"https://doi.org/10.37236/1143","mag":"1560563637"},"language":"en","primary_location":{"id":"doi:10.37236/1143","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1143","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1n5/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1n5/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044242774","display_name":"Catalin Zara","orcid":null},"institutions":[{"id":"https://openalex.org/I2800558167","display_name":"UPMC Altoona","ror":"https://ror.org/01mkye871","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I2800558167","https://openalex.org/I4210098814","https://openalex.org/I4210134769"]},{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Catalin Zara","raw_affiliation_strings":["Department Mathematics and Statistics Penn State Altoona, Altoona, PA"],"affiliations":[{"raw_affiliation_string":"Department Mathematics and Statistics Penn State Altoona, Altoona, PA","institution_ids":["https://openalex.org/I2800558167","https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5044242774"],"corresponding_institution_ids":["https://openalex.org/I130769515","https://openalex.org/I2800558167"],"apc_list":null,"apc_paid":null,"fwci":0.946,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.68168421,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"1","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/T11428","display_name":"Advanced Mathematical Identities","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/mathematics","display_name":"Mathematics","score":0.855472207069397},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8091112375259399},{"id":"https://openalex.org/keywords/bruhat-order","display_name":"Bruhat order","score":0.617811918258667},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.600661039352417},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.5813901424407959},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5304459929466248},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.24733439087867737},{"id":"https://openalex.org/keywords/weyl-group","display_name":"Weyl group","score":0.08868640661239624}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.855472207069397},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8091112375259399},{"id":"https://openalex.org/C177274530","wikidata":"https://www.wikidata.org/wiki/Q4978697","display_name":"Bruhat order","level":3,"score":0.617811918258667},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.600661039352417},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.5813901424407959},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5304459929466248},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.24733439087867737},{"id":"https://openalex.org/C40233952","wikidata":"https://www.wikidata.org/wiki/Q768074","display_name":"Weyl group","level":2,"score":0.08868640661239624},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/1143","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1143","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1n5/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.175.8505","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.175.8505","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_13/PDF/v13i1n5.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1143","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1143","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1n5/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320313188","display_name":"University of Massachusetts Boston","ror":"https://ror.org/04ydmy275"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1560563637.pdf","grobid_xml":"https://content.openalex.org/works/W1560563637.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W112671161","https://openalex.org/W1597069551","https://openalex.org/W1652980716","https://openalex.org/W2009190506"],"related_works":["https://openalex.org/W2951923925","https://openalex.org/W4229082010","https://openalex.org/W2950766725","https://openalex.org/W2980963558","https://openalex.org/W4386501576","https://openalex.org/W3170345835","https://openalex.org/W2002282073","https://openalex.org/W1882246857","https://openalex.org/W2349728712","https://openalex.org/W2980438719"],"abstract_inverted_index":{"Let":[0],"$S_n$":[1,13],"be":[2],"the":[3,42,51,58],"group":[4],"of":[5,7,37,46,61],"permutations":[6],"$[n]=\\{1,\\ldots,n\\}$.":[8],"The":[9],"Bruhat":[10],"order":[11,17],"on":[12,31],"is":[14],"a":[15],"partial":[16],"relation,":[18],"for":[19],"which":[20],"there":[21],"are":[22,29,55],"several":[23],"equivalent":[24,53],"definitions.":[25],"Three":[26],"well-known":[27],"conditions":[28,54],"based":[30],"ascending":[32],"chains,":[33],"subwords,":[34],"and":[35,48],"comparison":[36],"matrices,":[38],"respectively.":[39],"We":[40],"express":[41],"last":[43],"using":[44],"fillings":[45],"tableaux,":[47],"prove":[49],"that":[50],"three":[52],"satisfied":[56],"in":[57],"same":[59],"number":[60],"ways.":[62]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}