{"id":"https://openalex.org/W2964307804","doi":"https://doi.org/10.1090/mcom/3392","title":"Polynomial braid combing","display_name":"Polynomial braid combing","publication_year":2018,"publication_date":"2018-07-25","ids":{"openalex":"https://openalex.org/W2964307804","doi":"https://doi.org/10.1090/mcom/3392","mag":"2964307804"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3392","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3392","pdf_url":"https://www.ams.org/mcom/2019-88-318/S0025-5718-2018-03392-0/S0025-5718-2018-03392-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2019-88-318/S0025-5718-2018-03392-0/S0025-5718-2018-03392-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060519408","display_name":"Juan Gonz\u00e1lez-Meneses","orcid":"https://orcid.org/0000-0002-2520-2755"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Juan Gonz\u00e1lez-Meneses","raw_affiliation_strings":["Departamento de \u00c3\u0081lgebra, Facultad de Matem\u00c3\u00a1ticas, Instituto de Matem\u00c3\u00a1ticas (IMUS), Universidad de Sevilla, Av. Reina Mercedes s/n, 41012 Sevilla, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de \u00c3\u0081lgebra, Facultad de Matem\u00c3\u00a1ticas, Instituto de Matem\u00c3\u00a1ticas (IMUS), Universidad de Sevilla, Av. Reina Mercedes s/n, 41012 Sevilla, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058755150","display_name":"Marithania Silvero","orcid":"https://orcid.org/0000-0002-9786-0650"},"institutions":[{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"government","lineage":["https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Marithania Silvero","raw_affiliation_strings":["Institute of Mathematics, Polish Academy of Sciences, ul. \u00c5\u009aniadeckich, 8, 00-656 Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Polish Academy of Sciences, ul. \u00c5\u009aniadeckich, 8, 00-656 Warsaw, Poland","institution_ids":["https://openalex.org/I99542240","https://openalex.org/I4210137370"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5060519408"],"corresponding_institution_ids":["https://openalex.org/I79238269"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.29618662,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"88","issue":"318","first_page":"2027","last_page":"2045"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10304","display_name":"Geometric and Algebraic Topology","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9905999898910522,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9898999929428101,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/braid","display_name":"Braid","score":0.9619748592376709},{"id":"https://openalex.org/keywords/combing","display_name":"Combing","score":0.8384140729904175},{"id":"https://openalex.org/keywords/braid-group","display_name":"Braid group","score":0.7982485294342041},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7461389899253845},{"id":"https://openalex.org/keywords/braid-theory","display_name":"Braid theory","score":0.6644592881202698},{"id":"https://openalex.org/keywords/word-problem","display_name":"Word problem (mathematics education)","score":0.5085018873214722},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5080616474151611},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4737218916416168},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.45860111713409424},{"id":"https://openalex.org/keywords/section","display_name":"Section (typography)","score":0.45811763405799866},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37546873092651367},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34656354784965515},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1588205099105835},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1222091019153595},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.06309226155281067}],"concepts":[{"id":"https://openalex.org/C124194741","wikidata":"https://www.wikidata.org/wiki/Q320809","display_name":"Braid","level":2,"score":0.9619748592376709},{"id":"https://openalex.org/C2778952367","wikidata":"https://www.wikidata.org/wiki/Q3491532","display_name":"Combing","level":2,"score":0.8384140729904175},{"id":"https://openalex.org/C33840335","wikidata":"https://www.wikidata.org/wiki/Q220409","display_name":"Braid group","level":2,"score":0.7982485294342041},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7461389899253845},{"id":"https://openalex.org/C147441545","wikidata":"https://www.wikidata.org/wiki/Q220409","display_name":"Braid theory","level":3,"score":0.6644592881202698},{"id":"https://openalex.org/C90988201","wikidata":"https://www.wikidata.org/wiki/Q255912","display_name":"Word problem (mathematics education)","level":2,"score":0.5085018873214722},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5080616474151611},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4737218916416168},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.45860111713409424},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.45811763405799866},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37546873092651367},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34656354784965515},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1588205099105835},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1222091019153595},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.06309226155281067},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/3392","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3392","pdf_url":"https://www.ams.org/mcom/2019-88-318/S0025-5718-2018-03392-0/S0025-5718-2018-03392-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/mcom/3392","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3392","pdf_url":"https://www.ams.org/mcom/2019-88-318/S0025-5718-2018-03392-0/S0025-5718-2018-03392-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G201544605","display_name":null,"funder_award_id":"MTM2016-76453-C2-1-P","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G295860487","display_name":null,"funder_award_id":"MTM2013-44233-P","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"}],"funders":[{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2964307804.pdf","grobid_xml":"https://content.openalex.org/works/W2964307804.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1510722254","https://openalex.org/W1516116134","https://openalex.org/W1525312156","https://openalex.org/W1537551915","https://openalex.org/W1538868153","https://openalex.org/W1561337879","https://openalex.org/W1603550723","https://openalex.org/W1980694977","https://openalex.org/W2006091097","https://openalex.org/W2006823362","https://openalex.org/W2015978050","https://openalex.org/W2016758898","https://openalex.org/W2072733192","https://openalex.org/W2076505256","https://openalex.org/W2092501239","https://openalex.org/W2163650233","https://openalex.org/W2252831192","https://openalex.org/W2327745271","https://openalex.org/W3040586665","https://openalex.org/W3104047941","https://openalex.org/W6667375292"],"related_works":["https://openalex.org/W1859278099","https://openalex.org/W4298849474","https://openalex.org/W4363678311","https://openalex.org/W2951598886","https://openalex.org/W1846674139","https://openalex.org/W2094080661","https://openalex.org/W2153982254","https://openalex.org/W3037178427","https://openalex.org/W2945083448","https://openalex.org/W1550066936"],"abstract_inverted_index":{"Braid":[0],"combing":[1,86],"is":[2,18],"a":[3,38,90,104,117],"procedure":[4,46,144],"defined":[5],"by":[6,110],"Emil":[7],"Artin":[8],"to":[9,21,36,50,88,99,108,145],"solve":[10],"the":[11,30,55,63,79,93,97,100,135,142],"word":[12,64],"problem":[13,65],"in":[14,73,130,148,154],"braid":[15,43,67,85,101,136],"groups.":[16],"It":[17],"well":[19],"known":[20],"have":[22],"exponential":[23],"complexity.":[24],"In":[25,78],"this":[26,155],"paper,":[27],"we":[28,127,139],"use":[29,89],"theory":[31],"of":[32,81,96,132,134],"straight":[33],"line":[34],"programs":[35],"give":[37],"polynomial":[39,74,149],"algorithm":[40,57],"which":[41,61,126],"performs":[42],"combing.":[44],"This":[45],"can":[47],"be":[48],"applied":[49],"braids":[51,147],"on":[52,69],"surfaces,":[53],"providing":[54],"first":[56],"(to":[58],"our":[59],"knowledge)":[60],"solves":[62],"for":[66],"groups":[68],"surfaces":[70,82],"with":[71],"boundary":[72],"time":[75,150],"and":[76,112,138],"space.":[77],"case":[80],"without":[83],"boundary,":[84],"needs":[87],"section":[91,105],"from":[92],"fundamental":[94],"group":[95],"surface":[98],"group.":[102],"Such":[103],"was":[106],"shown":[107],"exist":[109],"Gon\u00e7alves":[111],"Guaschi,":[113],"who":[114],"also":[115],"gave":[116],"geometric":[118],"description.":[119],"We":[120],"propose":[121],"an":[122],"algebraically":[123],"simpler":[124],"section,":[125],"describe":[128],"explicitly":[129],"terms":[131],"generators":[133],"group,":[137],"show":[140],"why":[141],"above":[143],"comb":[146],"does":[151],"not":[152],"work":[153],"case.":[156]},"counts_by_year":[],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}
