{"id":"https://openalex.org/W1560615206","doi":"https://doi.org/10.37236/3861","title":"Bruhat Order on Fixed-Point-Free Involutions in the Symmetric Group","display_name":"Bruhat Order on Fixed-Point-Free Involutions in the Symmetric Group","publication_year":2014,"publication_date":"2014-05-02","ids":{"openalex":"https://openalex.org/W1560615206","doi":"https://doi.org/10.37236/3861","mag":"1560615206"},"language":"en","primary_location":{"id":"doi:10.37236/3861","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3861","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i2p20/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/v21i2p20/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102292132","display_name":"Matthew A. Watson","orcid":null},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Matthew Watson","raw_affiliation_strings":["North Carolina State University","North Carolina State University,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"North Carolina State University","institution_ids":["https://openalex.org/I137902535"]},{"raw_affiliation_string":"North Carolina State University,","institution_ids":["https://openalex.org/I137902535"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5102292132"],"corresponding_institution_ids":["https://openalex.org/I137902535"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.04429302,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"21","issue":"2","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":0.9994999766349792,"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":0.9994999766349792,"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":0.993399977684021,"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/T11716","display_name":"Random Matrices and Applications","score":0.9850000143051147,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/combinatorial-proof","display_name":"Combinatorial proof","score":0.8435061573982239},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8388832807540894},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.828004002571106},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.6379460692405701},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.6129345297813416},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.5429328680038452},{"id":"https://openalex.org/keywords/catalan-number","display_name":"Catalan number","score":0.5366790294647217},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.49622708559036255},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4496125876903534},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.42863041162490845},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.42562249302864075},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.42112818360328674},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.362729549407959}],"concepts":[{"id":"https://openalex.org/C118539577","wikidata":"https://www.wikidata.org/wiki/Q3402784","display_name":"Combinatorial proof","level":2,"score":0.8435061573982239},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8388832807540894},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.828004002571106},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.6379460692405701},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.6129345297813416},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.5429328680038452},{"id":"https://openalex.org/C43929256","wikidata":"https://www.wikidata.org/wiki/Q270513","display_name":"Catalan number","level":2,"score":0.5366790294647217},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.49622708559036255},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4496125876903534},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.42863041162490845},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.42562249302864075},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.42112818360328674},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.362729549407959},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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":1,"locations":[{"id":"doi:10.37236/3861","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3861","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i2p20/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/3861","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3861","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i2p20/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.699999988079071,"display_name":"Life in Land"}],"awards":[{"id":"https://openalex.org/G2870963262","display_name":"EMSW21-MCTP: Institute for Mathematics at North Carolina State University. (I'M at State)","funder_award_id":"0943855","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/F4320310013","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1560615206.pdf","grobid_xml":"https://content.openalex.org/works/W1560615206.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W112671161","https://openalex.org/W2046116901","https://openalex.org/W2131397279","https://openalex.org/W2752061190","https://openalex.org/W2911361414","https://openalex.org/W2952131905","https://openalex.org/W2962935317","https://openalex.org/W4300302225"],"related_works":["https://openalex.org/W1557127993","https://openalex.org/W3000541016","https://openalex.org/W1560615206","https://openalex.org/W2134039502","https://openalex.org/W3098015730","https://openalex.org/W2788864678","https://openalex.org/W2086188043","https://openalex.org/W2963926465","https://openalex.org/W2629848946","https://openalex.org/W2963919342"],"abstract_inverted_index":{"We":[0],"provide":[1],"a":[2,22,26,42,48,54,74],"structural":[3],"description":[4],"of":[5,12,25,33,53,61,73],"Bruhat":[6],"order":[7],"on":[8,64],"the":[9,16,59,65],"set":[10],"$F_{2n}$":[11],"fixed-point-free":[13],"involutions":[14],"in":[15],"symetric":[17],"group":[18],"$S_{2n}$":[19],"which":[20,46],"yields":[21,47],"combinatorial":[23,27,55,86],"proof":[24,52],"identity":[28,56],"that":[29,57,88],"is":[30,39],"an":[31],"expansion":[32],"its":[34],"rank-generating":[35],"function.":[36],"The":[37],"decomposition":[38],"accomplished":[40],"via":[41],"natural":[43],"poset":[44],"congruence,":[45],"new":[49,85],"interpretation":[50],"and":[51,98],"counts":[58],"number":[60],"rook":[62],"placements":[63],"Ferrers":[66],"boards":[67],"lying":[68],"under":[69],"all":[70],"Dyck":[71],"paths":[72],"given":[75],"length":[76],"$2n$.":[77],"Additionally,":[78],"this":[79],"result":[80],"extends":[81],"naturally":[82],"to":[83],"prove":[84],"identities":[87],"sum":[89],"over":[90],"other":[91],"Catalan":[92],"objects:":[93],"312-avoiding":[94],"permutations,":[95],"plane":[96],"forests,":[97],"binary":[99],"trees.":[100]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-06-03T06:16:58.514037","created_date":"2025-10-10T00:00:00"}