{"id":"https://openalex.org/W2101596584","doi":"https://doi.org/10.1051/ita:2008006","title":"Least Periods of Factors of Infinite Words","display_name":"Least Periods of Factors of Infinite Words","publication_year":2008,"publication_date":"2008-03-11","ids":{"openalex":"https://openalex.org/W2101596584","doi":"https://doi.org/10.1051/ita:2008006","mag":"2101596584"},"language":"en","primary_location":{"id":"doi:10.1051/ita:2008006","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita:2008006","pdf_url":null,"source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X","2804-7346"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10680/1372","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","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 D. Currie","raw_affiliation_strings":["Department of Mathematics & Statistics, University of Winnipeg, Winnipeg, R3B2E9, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics & Statistics, University of Winnipeg, Winnipeg, R3B2E9, Canada","institution_ids":["https://openalex.org/I872945872"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008095510","display_name":"Kalle Saari","orcid":null},"institutions":[{"id":"https://openalex.org/I183173800","display_name":"Turku Centre for Computer Science","ror":"https://ror.org/00vy7ed73","country_code":"FI","type":"facility","lineage":["https://openalex.org/I130217899","https://openalex.org/I155660961","https://openalex.org/I183173800"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Kalle Saari","raw_affiliation_strings":["Department of Mathematics and Turku Centre for Computer Science, University of Turku, Turku, Finland; kasaar@utu.fi"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Turku Centre for Computer Science, University of Turku, Turku, Finland; kasaar@utu.fi","institution_ids":["https://openalex.org/I183173800"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1811,"has_fulltext":false,"cited_by_count":51,"citation_normalized_percentile":{"value":0.80938161,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"43","issue":"1","first_page":"165","last_page":"178"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9940000176429749,"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/T10911","display_name":"Chemical Synthesis and Analysis","score":0.9818000197410583,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fibonacci-number","display_name":"Fibonacci number","score":0.9158040285110474},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.7632713317871094},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7631231546401978},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.694837212562561},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6941823959350586},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6074730753898621},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5806801915168762},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.503861129283905},{"id":"https://openalex.org/keywords/factor","display_name":"Factor (programming language)","score":0.44032683968544006},{"id":"https://openalex.org/keywords/infinite-set","display_name":"Infinite set","score":0.4292071759700775},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4033510982990265},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3307778835296631},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13044586777687073}],"concepts":[{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.9158040285110474},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.7632713317871094},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7631231546401978},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.694837212562561},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6941823959350586},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6074730753898621},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5806801915168762},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.503861129283905},{"id":"https://openalex.org/C2781039887","wikidata":"https://www.wikidata.org/wiki/Q1391724","display_name":"Factor (programming language)","level":2,"score":0.44032683968544006},{"id":"https://openalex.org/C199879729","wikidata":"https://www.wikidata.org/wiki/Q205140","display_name":"Infinite set","level":3,"score":0.4292071759700775},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4033510982990265},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3307778835296631},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13044586777687073},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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":3,"locations":[{"id":"doi:10.1051/ita:2008006","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita:2008006","pdf_url":null,"source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X","2804-7346"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","raw_type":"journal-article"},{"id":"pmh:oai:numdam.org:ITA_2009__43_1_165_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ita:2008006/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"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"},{"id":"pmh:oai:winnspace.uwinnipeg.ca:10680/1372","is_oa":true,"landing_page_url":"http://hdl.handle.net/10680/1372","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":"pmh:oai:winnspace.uwinnipeg.ca:10680/1372","is_oa":true,"landing_page_url":"http://hdl.handle.net/10680/1372","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W3242420","https://openalex.org/W137071685","https://openalex.org/W1514324498","https://openalex.org/W1526693856","https://openalex.org/W1586417893","https://openalex.org/W1853820275","https://openalex.org/W1968329633","https://openalex.org/W1987261421","https://openalex.org/W1998239737","https://openalex.org/W2035314514","https://openalex.org/W2047088605","https://openalex.org/W2053586427","https://openalex.org/W2070037875","https://openalex.org/W4231199984"],"related_works":["https://openalex.org/W2920386017","https://openalex.org/W2795454383","https://openalex.org/W4317662907","https://openalex.org/W2054041134","https://openalex.org/W1965364641","https://openalex.org/W4316467349","https://openalex.org/W2896847511","https://openalex.org/W199458103","https://openalex.org/W2369612463","https://openalex.org/W2752116162"],"abstract_inverted_index":{"We":[0,17],"show":[1],"that":[2],"any":[3],"positive":[4],"integer":[5],"is":[6,40],"the":[7,14,20,33,37,41],"least":[8,23],"period":[9],"of":[10,13,22,25,27,43,49,59,62],"a":[11,28,47],"factor":[12],"Thue-Morse":[15],"word.":[16,30],"also":[18],"characterize":[19],"set":[21,35,42],"periods":[24],"factors":[26],"Sturmian":[29,63],"In":[31],"particular,":[32],"corresponding":[34],"for":[36],"Fibonacci":[38,44],"word":[39],"numbers.":[45],"As":[46],"by-product":[48],"our":[50],"results,":[51],"we":[52],"give":[53],"several":[54],"new":[55],"proofs":[56],"and":[57],"tightenings":[58],"well-known":[60],"properties":[61],"words.":[64]},"counts_by_year":[{"year":2026,"cited_by_count":16},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}
