{"id":"https://openalex.org/W2789530262","doi":"https://doi.org/10.1142/s0218196718500157","title":"Elementary equivalence in Artin groups of finite type","display_name":"Elementary equivalence in Artin groups of finite type","publication_year":2018,"publication_date":"2018-02-13","ids":{"openalex":"https://openalex.org/W2789530262","doi":"https://doi.org/10.1142/s0218196718500157","mag":"2789530262"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196718500157","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196718500157","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1707.08353","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088606994","display_name":"Arpan Kabiraj","orcid":"https://orcid.org/0000-0002-5846-7688"},"institutions":[{"id":"https://openalex.org/I19149307","display_name":"Chennai Mathematical Institute","ror":"https://ror.org/04zp24820","country_code":"IN","type":"education","lineage":["https://openalex.org/I19149307"]},{"id":"https://openalex.org/I6498739","display_name":"Indian Statistical Institute","ror":"https://ror.org/00q2w1j53","country_code":"IN","type":"education","lineage":["https://openalex.org/I6498739"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Arpan Kabiraj","raw_affiliation_strings":["Chennai Mathematical Institute, India","Indian Statistical Institute, Chennai, India","Chennai Mathematical Institute , Chennai , India"],"affiliations":[{"raw_affiliation_string":"Chennai Mathematical Institute, India","institution_ids":["https://openalex.org/I19149307"]},{"raw_affiliation_string":"Indian Statistical Institute, Chennai, India","institution_ids":["https://openalex.org/I6498739"]},{"raw_affiliation_string":"Chennai Mathematical Institute , Chennai , India","institution_ids":["https://openalex.org/I19149307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058907676","display_name":"T. V. H. Prathamesh","orcid":null},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]},{"id":"https://openalex.org/I19149307","display_name":"Chennai Mathematical Institute","ror":"https://ror.org/04zp24820","country_code":"IN","type":"education","lineage":["https://openalex.org/I19149307"]},{"id":"https://openalex.org/I6498739","display_name":"Indian Statistical Institute","ror":"https://ror.org/00q2w1j53","country_code":"IN","type":"education","lineage":["https://openalex.org/I6498739"]}],"countries":["AT","IN"],"is_corresponding":false,"raw_author_name":"T. V. H. Prathamesh","raw_affiliation_strings":["University of Innsbruck, Austria","Chennai Mathematical Institute , Chennai , India","Indian Statistical Institute, Chennai, India"],"affiliations":[{"raw_affiliation_string":"University of Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]},{"raw_affiliation_string":"Chennai Mathematical Institute , Chennai , India","institution_ids":["https://openalex.org/I19149307"]},{"raw_affiliation_string":"Indian Statistical Institute, Chennai, India","institution_ids":["https://openalex.org/I6498739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091032397","display_name":"Rishi Vyas","orcid":null},"institutions":[{"id":"https://openalex.org/I19149307","display_name":"Chennai Mathematical Institute","ror":"https://ror.org/04zp24820","country_code":"IN","type":"education","lineage":["https://openalex.org/I19149307"]},{"id":"https://openalex.org/I6498739","display_name":"Indian Statistical Institute","ror":"https://ror.org/00q2w1j53","country_code":"IN","type":"education","lineage":["https://openalex.org/I6498739"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Rishi Vyas","raw_affiliation_strings":["Chennai Mathematical Institute , Chennai , India","Indian Statistical Institute, Chennai, India"],"affiliations":[{"raw_affiliation_string":"Chennai Mathematical Institute , Chennai , India","institution_ids":["https://openalex.org/I19149307"]},{"raw_affiliation_string":"Indian Statistical Institute, Chennai, India","institution_ids":["https://openalex.org/I6498739"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5088606994"],"corresponding_institution_ids":["https://openalex.org/I19149307","https://openalex.org/I6498739"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09319678,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"02","first_page":"331","last_page":"344"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9998999834060669,"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":0.9998999834060669,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9922999739646912,"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"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9878000020980835,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9386390447616577},{"id":"https://openalex.org/keywords/coxeter-group","display_name":"Coxeter group","score":0.7371430397033691},{"id":"https://openalex.org/keywords/braid-group","display_name":"Braid group","score":0.6388412117958069},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.58992999792099},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5641303658485413},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5036007761955261},{"id":"https://openalex.org/keywords/group-isomorphism","display_name":"Group isomorphism","score":0.5035731196403503},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5031155943870544},{"id":"https://openalex.org/keywords/artin-group","display_name":"Artin group","score":0.4992034435272217},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4683589041233063},{"id":"https://openalex.org/keywords/outer-automorphism-group","display_name":"Outer automorphism group","score":0.13653552532196045},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.13523036241531372},{"id":"https://openalex.org/keywords/automorphism-group","display_name":"Automorphism group","score":0.12689310312271118}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9386390447616577},{"id":"https://openalex.org/C143669375","wikidata":"https://www.wikidata.org/wiki/Q7874246","display_name":"Coxeter group","level":2,"score":0.7371430397033691},{"id":"https://openalex.org/C33840335","wikidata":"https://www.wikidata.org/wiki/Q220409","display_name":"Braid group","level":2,"score":0.6388412117958069},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.58992999792099},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5641303658485413},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5036007761955261},{"id":"https://openalex.org/C155190451","wikidata":"https://www.wikidata.org/wiki/Q742064","display_name":"Group isomorphism","level":5,"score":0.5035731196403503},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5031155943870544},{"id":"https://openalex.org/C201064014","wikidata":"https://www.wikidata.org/wiki/Q3956993","display_name":"Artin group","level":3,"score":0.4992034435272217},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4683589041233063},{"id":"https://openalex.org/C7619685","wikidata":"https://www.wikidata.org/wiki/Q3630548","display_name":"Outer automorphism group","level":4,"score":0.13653552532196045},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.13523036241531372},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.12689310312271118},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218196718500157","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196718500157","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1707.08353","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1707.08353","pdf_url":"https://arxiv.org/pdf/1707.08353","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1707.08353","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1707.08353","pdf_url":"https://arxiv.org/pdf/1707.08353","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W296038034","https://openalex.org/W1584901588","https://openalex.org/W1964103416","https://openalex.org/W1978423759","https://openalex.org/W1979727105","https://openalex.org/W2005047182","https://openalex.org/W2020502548","https://openalex.org/W2036334014","https://openalex.org/W2048470146","https://openalex.org/W2055422279","https://openalex.org/W2081925316","https://openalex.org/W2158446505","https://openalex.org/W2334447217","https://openalex.org/W3031113357","https://openalex.org/W3104583765","https://openalex.org/W4249274673"],"related_works":["https://openalex.org/W4225948823","https://openalex.org/W4221141486","https://openalex.org/W2137401377","https://openalex.org/W4387106546","https://openalex.org/W2087186172","https://openalex.org/W2068996638","https://openalex.org/W4283321120","https://openalex.org/W2070976151","https://openalex.org/W2063650011","https://openalex.org/W4367043192"],"abstract_inverted_index":{"Irreducible":[0],"Artin":[1,137],"groups":[2,59,92,116,138,148,158],"of":[3,23,34,51,114,122,135,139,149,156],"finite":[4,140],"type":[5],"can":[6],"be":[7],"parametrized":[8,27],"via":[9],"their":[10],"associated":[11],"Coxeter":[12],"diagrams":[13],"into":[14],"six":[15],"sporadic":[16],"examples":[17],"and":[18,46,67,97,164],"four":[19,36,53],"infinite":[20,37],"families,":[21,38,54],"each":[22,33],"which":[24],"is":[25,78],"further":[26],"by":[28],"the":[29,41,52,61,82,111,115],"natural":[30],"numbers.":[31],"Within":[32],"these":[35],"we":[39,55,87,125],"investigate":[40],"relationship":[42],"between":[43],"elementary":[44,112,132],"equivalence":[45,133],"isomorphism.":[47],"For":[48],"three":[49],"out":[50],"show":[56,88,144],"that":[57,89,127,145],"two":[58,90],"in":[60,117],"same":[62],"family":[63],"are":[64,71,93,101,129,160,168],"equivalent":[65,95,162],"if":[66,69,96,99,163,166],"only":[68,98,165],"they":[70,100,167],"isomorphic;":[72],"a":[73,120,153],"positive,":[74],"but":[75],"weaker,":[76],"result":[77],"also":[79,143],"attained":[80],"for":[81],"fourth":[83],"family.":[84],"In":[85],"particular,":[86],"braid":[91,157],"elementarily":[94,161],"isomorphic.":[102,169],"The":[103],"[Formula:":[104],"see":[105],"text]":[106],"fragment":[107],"suffices":[108],"to":[109],"distinguish":[110],"theories":[113],"question.":[118],"As":[119],"consequence":[121],"our":[123],"work,":[124],"prove":[126],"there":[128],"infinitely":[130],"many":[131],"classes":[134],"irreducible":[136],"type.":[141],"We":[142],"mapping":[146],"class":[147],"closed":[150],"surfaces":[151],"\u2014":[152,159],"geometric":[154],"analogue":[155]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}