{"id":"https://openalex.org/W2136058931","doi":"https://doi.org/10.37236/1365","title":"Extremal Infinite Overlap-Free Binary Words","display_name":"Extremal Infinite Overlap-Free Binary Words","publication_year":1998,"publication_date":"1998-05-03","ids":{"openalex":"https://openalex.org/W2136058931","doi":"https://doi.org/10.37236/1365","mag":"2136058931"},"language":"en","primary_location":{"id":"doi:10.37236/1365","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1365","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v5i1r27/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":false,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v5i1r27/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018323679","display_name":"Jean\u2010Paul Allouche","orcid":"https://orcid.org/0000-0002-9060-0784"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210097733","display_name":"Laboratoire de Physique Th\u00e9orique et Mod\u00e8les Statistiques","ror":"https://ror.org/00w67e447","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4210097733"]},{"id":"https://openalex.org/I4210144804","display_name":"Laboratoire de Recherche en Informatique","ror":"https://ror.org/04e3ktk27","country_code":"FR","type":"facility","lineage":["https://openalex.org/I102197404","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210144804","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean-Paul Allouche","raw_affiliation_strings":["CNRS, LRI Btiment 490 F-91405 Orsay Cedex (France)","CNRS, LRI B\u00e2timent 490 F-91405 Orsay Cedex (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS, LRI Btiment 490 F-91405 Orsay Cedex (France)","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210097733","https://openalex.org/I4210144804"]},{"raw_affiliation_string":"CNRS, LRI B\u00e2timent 490 F-91405 Orsay Cedex (France)","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210144804"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065770361","display_name":"James D. Currie","orcid":"https://orcid.org/0000-0002-0061-3849"},"institutions":[{"id":"https://openalex.org/I872945872","display_name":"University of Winnipeg","ror":"https://ror.org/02gdzyx04","country_code":"CA","type":"education","lineage":["https://openalex.org/I872945872"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"James Currie","raw_affiliation_strings":["Department of Mathematics University of Winnipeg Winnipeg, Manitoba R3B 2E9 (Canada)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Winnipeg Winnipeg, Manitoba R3B 2E9 (Canada)","institution_ids":["https://openalex.org/I872945872"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065322269","display_name":"Jeffrey Shallit","orcid":"https://orcid.org/0000-0003-1197-3820"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Jeffrey Shallit","raw_affiliation_strings":["Department of Computer Science University of Waterloo Waterloo, Ontario N2L 3G1 (Canada)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science University of Waterloo Waterloo, Ontario N2L 3G1 (Canada)","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4611,"has_fulltext":true,"cited_by_count":27,"citation_normalized_percentile":{"value":0.8309999,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"5","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lexicographical-order","display_name":"Lexicographical order","score":0.8507537841796875},{"id":"https://openalex.org/keywords/suffix","display_name":"Suffix","score":0.8037647008895874},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7725027799606323},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7467367649078369},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.6936661005020142},{"id":"https://openalex.org/keywords/morphism","display_name":"Morphism","score":0.6557005643844604},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.6124468445777893},{"id":"https://openalex.org/keywords/prefix","display_name":"Prefix","score":0.5707012414932251},{"id":"https://openalex.org/keywords/combinatorics-on-words","display_name":"Combinatorics on words","score":0.45214706659317017},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41233834624290466},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3162909150123596},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.055029064416885376}],"concepts":[{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.8507537841796875},{"id":"https://openalex.org/C2779804580","wikidata":"https://www.wikidata.org/wiki/Q102047","display_name":"Suffix","level":2,"score":0.8037647008895874},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7725027799606323},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7467367649078369},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.6936661005020142},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.6557005643844604},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.6124468445777893},{"id":"https://openalex.org/C141603448","wikidata":"https://www.wikidata.org/wiki/Q134830","display_name":"Prefix","level":2,"score":0.5707012414932251},{"id":"https://openalex.org/C164804908","wikidata":"https://www.wikidata.org/wiki/Q2985058","display_name":"Combinatorics on words","level":3,"score":0.45214706659317017},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41233834624290466},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3162909150123596},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.055029064416885376},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/1365","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1365","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v5i1r27/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":false,"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:10.1.1.46.5271","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.5271","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_5/../Volume_5/PDF/v5i1r27.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.50.3622","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.3622","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_5/PostScriptfiles/v5i1r27.ps","raw_type":"text"},{"id":"pmh:oai:winnspace.uwinnipeg.ca:10680/1348","is_oa":true,"landing_page_url":"http://hdl.handle.net/10680/1348","pdf_url":null,"source":{"id":"https://openalex.org/S4306400200","display_name":"WinnSpace (University of Winnipeg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I872945872","host_organization_name":"University of Winnipeg","host_organization_lineage":["https://openalex.org/I872945872"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.37236/1365","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1365","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v5i1r27/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":false,"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/F4320322676","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2136058931.pdf","grobid_xml":"https://content.openalex.org/works/W2136058931.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W177169205","https://openalex.org/W1557522533","https://openalex.org/W1992016479","https://openalex.org/W2003927948","https://openalex.org/W2021093608","https://openalex.org/W2062993376","https://openalex.org/W2156169026","https://openalex.org/W2787696925","https://openalex.org/W3081952542","https://openalex.org/W3135788083","https://openalex.org/W4319451620"],"related_works":["https://openalex.org/W2055891180","https://openalex.org/W2022951409","https://openalex.org/W3196825089","https://openalex.org/W4368367671","https://openalex.org/W2413189204","https://openalex.org/W3012663989","https://openalex.org/W4385652842","https://openalex.org/W2773803767","https://openalex.org/W4381095475","https://openalex.org/W4318200119"],"abstract_inverted_index":{"Let":[0],"$\\overline{\\bf":[1,81],"t}$":[2],"be":[3,32],"the":[4,12,40,58,85],"infinite":[5,22,61,88],"fixed":[6],"point,":[7],"starting":[8],"with":[9,66],"$1$,":[10],"of":[11,39,80],"morphism":[13],"$\\mu:":[14],"0":[15],"\\rightarrow":[16,19],"01$,":[17],"$1":[18],"10$.":[20],"An":[21],"word":[23,64,91],"over":[24],"$\\lbrace":[25],"0,":[26],"1":[27],"\\rbrace$":[28,48],"is":[29,77,92],"said":[30],"to":[31],"overlap-free":[33,62,89],"if":[34,70],"it":[35,71],"contains":[36],"no":[37],"factor":[38],"form":[41],"$axaxa$,":[42],"where":[43],"$a":[44],"\\in":[45,51],"\\lbrace":[46,52],"0,1":[47,53],"and":[49],"$x":[50],"\\rbrace^*$.":[54],"We":[55],"prove":[56],"that":[57],"lexicographically":[59,86],"least":[60,87],"binary":[63,90],"beginning":[65],"any":[67],"specified":[68],"prefix,":[69],"exists,":[72],"has":[73],"a":[74,78],"suffix":[75,79],"which":[76],"t}$.":[82,95],"In":[83],"particular,":[84],"$001001":[93],"\\overline{\\bf":[94]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}