{"id":"https://openalex.org/W2048770839","doi":"https://doi.org/10.1142/s0218196793000196","title":"COMPUTING HALL EXPONENTS IN THE FREE GROUP","display_name":"COMPUTING HALL EXPONENTS IN THE FREE GROUP","publication_year":1993,"publication_date":"1993-09-01","ids":{"openalex":"https://openalex.org/W2048770839","doi":"https://doi.org/10.1142/s0218196793000196","mag":"2048770839"},"language":"fr","primary_location":{"id":"doi:10.1142/s0218196793000196","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196793000196","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":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070966718","display_name":"Guy M\u00e9lan\u00e7on","orcid":"https://orcid.org/0000-0003-3193-7261"},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]},{"id":"https://openalex.org/I4210142254","display_name":"Laboratoire Bordelais de Recherche en Informatique","ror":"https://ror.org/03adqg323","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210159245","https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"GUY MELAN\u00c7ON","raw_affiliation_strings":["LaBRI, Universit\u00e9 de Bordeaux I, 351, Cours de la Lib\u00e9ration, 33405 Talence Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LaBRI, Universit\u00e9 de Bordeaux I, 351, Cours de la Lib\u00e9ration, 33405 Talence Cedex, France","institution_ids":["https://openalex.org/I15057530","https://openalex.org/I4210142254"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038352414","display_name":"Christophe Reutenauer","orcid":"https://orcid.org/0000-0003-1739-3691"},"institutions":[{"id":"https://openalex.org/I159129438","display_name":"Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al","ror":"https://ror.org/002rjbv21","country_code":"CA","type":"education","lineage":["https://openalex.org/I159129438","https://openalex.org/I49663120"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"CHRISTOPHE REUTENAUER","raw_affiliation_strings":["LaCIM, D\u00e9partement de math. et info., Universit\u00e9 du Qu\u00e9bec a Montr\u00e9al, C.P. 8888, Succ. A, Montr\u00e9al (Qu\u00e9bec), Canada H3C 3P8, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LaCIM, D\u00e9partement de math. et info., Universit\u00e9 du Qu\u00e9bec a Montr\u00e9al, C.P. 8888, Succ. A, Montr\u00e9al (Qu\u00e9bec), Canada H3C 3P8, Canada","institution_ids":["https://openalex.org/I159129438"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.20554615,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"03","issue":"03","first_page":"275","last_page":"294"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.9958999752998352,"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"}},"topics":[{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.9958999752998352,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9944000244140625,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9921000003814697,"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":0.8290733098983765},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.43750500679016113},{"id":"https://openalex.org/keywords/free-product","display_name":"Free product","score":0.4302785098552704},{"id":"https://openalex.org/keywords/humanities","display_name":"Humanities","score":0.4037330746650696},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3640245795249939},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3263469338417053},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0971967875957489},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06206938624382019}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8290733098983765},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.43750500679016113},{"id":"https://openalex.org/C47527751","wikidata":"https://www.wikidata.org/wiki/Q1454165","display_name":"Free product","level":3,"score":0.4302785098552704},{"id":"https://openalex.org/C15708023","wikidata":"https://www.wikidata.org/wiki/Q80083","display_name":"Humanities","level":1,"score":0.4037330746650696},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3640245795249939},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3263469338417053},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0971967875957489},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06206938624382019},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196793000196","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196793000196","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2033330749","https://openalex.org/W2964342945"],"abstract_inverted_index":{"Nous":[0,22,45],"donnons":[1,87],"une":[2],"g\u00e9n\u00e9ralisation":[3],"de":[4,7,18,20,26,32,42,72,78,88,91,98,106],"la":[5,33,70,76,107],"d\u00e9composition":[6,34],"M.":[8,119],"Hall":[9,79,134,146,171,184],"des":[10,36,48],"\u00e9l\u00e9ments":[11,105],"du":[12,111],"groupe":[13,82],"libre":[14],"en":[15],"produits":[16],"d\u00e9croissant":[17],"commutateurs":[19],"Hall.":[21],"g\u00e9n\u00e9ralisons":[23],"les":[24,30,61,96,104],"identit\u00e9s":[25],"Th\u00e9rien,":[27],"qui":[28,63,102],"expriment":[29],"exposants":[31],"comme":[35],"sommes":[37],"\u00e0":[38],"coefficients":[39],"entiers":[40],"positifs":[41],"fonctions":[43,49,62,74],"sous-mots.":[44],"\u00e9tudions":[46],"l\u2019alg\u00e8bre":[47],"sous-mots":[50],"et":[51,100],"nous":[52,67,86],"montrons":[53,68],"que":[54],"cette":[55],"alg\u00e8bre":[56],"est":[57],"librement":[58],"engendr\u00e9e":[59],"par":[60],"donnent":[64],"ces":[65,73],"exposants;":[66],"aussi":[69],"continuit\u00e9":[71],"pour":[75],"topologie":[77],"sur":[80],"le":[81],"libre.":[83,113],"De":[84],"plus,":[85],"nouvelles":[89],"preuves":[90],"r\u00e9sultats":[92],"connus,":[93],"entre":[94],"autres":[95],"th\u00e9or\u00e8mes":[97],"Magnus":[99,205],"Witt":[101,207],"caract\u00e9risent":[103],"s\u00e9rie":[108],"centrale":[109],"descendante":[110],"grouple":[112],"We":[114,136,155],"give":[115,194],"the":[116,126,139,145,157,170,177,183,187,202,209,214],"generalization":[117,140],"of":[118,122,125,133,141,152,159,179,197,201,204,213],"Hall\u2019s":[120],"expansion":[121],"each":[123],"element":[124],"free":[127,188,215],"group":[128],"as":[129,148],"a":[130],"decreasing":[131],"product":[132],"commutators.":[135],"also":[137,175],"prove":[138,176],"Therien\u2019s":[142],"identities":[143],"expressing":[144],"exponents":[147,172],"nonnegative":[149],"linear":[150],"combinations":[151],"subword":[153,160],"functions.":[154],"study":[156],"algebra":[158],"functions":[161,181],"and":[162,206],"show":[163],"that":[164],"it":[165],"is":[166],"freely":[167],"generated":[168],"by":[169],"functions;":[173],"we":[174,193],"continuity":[178],"these":[180,191],"for":[182],"topology":[185],"on":[186,208],"group.":[189,216],"Besides":[190],"results,":[192,199],"new":[195],"proofs":[196],"known":[198],"especially":[200],"theorem":[203],"lower":[210],"central":[211],"series":[212]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}