{"id":"https://openalex.org/W1976449761","doi":"https://doi.org/10.1051/ita/2014020","title":"5-Abelian cubes are avoidable on binary alphabets","display_name":"5-Abelian cubes are avoidable on binary alphabets","publication_year":2014,"publication_date":"2014-07-31","ids":{"openalex":"https://openalex.org/W1976449761","doi":"https://doi.org/10.1051/ita/2014020","mag":"1976449761"},"language":"en","primary_location":{"id":"doi:10.1051/ita/2014020","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita/2014020","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":"https://www.numdam.org/item/10.1051/ita/2014020.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049507611","display_name":"Robert Merca\u015f","orcid":"https://orcid.org/0000-0001-6034-433X"},"institutions":[{"id":"https://openalex.org/I32021983","display_name":"Christian-Albrechts-Universit\u00e4t zu Kiel","ror":"https://ror.org/04v76ef78","country_code":"DE","type":"education","lineage":["https://openalex.org/I32021983"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Robert Merca\u015f","raw_affiliation_strings":["Christian-Albrechts-Universit\u00e4t zu Kiel, Institut f\u00fcr Informatik, 24098 Kiel, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Christian-Albrechts-Universit\u00e4t zu Kiel, Institut f\u00fcr Informatik, 24098 Kiel, Germany","institution_ids":["https://openalex.org/I32021983"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031862611","display_name":"Aleksi Saarela","orcid":"https://orcid.org/0000-0002-6636-2317"},"institutions":[{"id":"https://openalex.org/I155660961","display_name":"University of Turku","ror":"https://ror.org/05vghhr25","country_code":"FI","type":"education","lineage":["https://openalex.org/I155660961"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Aleksi Saarela","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Turku, 20014 Turku, Finland","Department of Mathematics and Statistics; University of Turku; 20014 Turku Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Turku, 20014 Turku, Finland","institution_ids":["https://openalex.org/I155660961"]},{"raw_affiliation_string":"Department of Mathematics and Statistics; University of Turku; 20014 Turku Finland","institution_ids":["https://openalex.org/I155660961"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7461,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.83897169,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"48","issue":"4","first_page":"467","last_page":"478"},"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/T12029","display_name":"DNA and Biological Computing","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9991000294685364,"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/abelian-group","display_name":"Abelian group","score":0.8696492314338684},{"id":"https://openalex.org/keywords/cube","display_name":"Cube (algebra)","score":0.6939347386360168},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6664018034934998},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.6140581965446472},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.6090115308761597},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5528794527053833},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.5221412777900696},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.5053206086158752},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37755322456359863},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.23485910892486572},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0748583972454071},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.04580610990524292},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.04095754027366638},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.03785714507102966}],"concepts":[{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.8696492314338684},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.6939347386360168},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6664018034934998},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.6140581965446472},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.6090115308761597},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5528794527053833},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.5221412777900696},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.5053206086158752},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37755322456359863},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.23485910892486572},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0748583972454071},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.04580610990524292},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.04095754027366638},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.03785714507102966}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1051/ita/2014020","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita/2014020","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_2014__48_4_467_0","is_oa":true,"landing_page_url":"http://www.numdam.org/articles/10.1051/ita/2014020/","pdf_url":"https://www.numdam.org/item/10.1051/ita/2014020.pdf","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"}],"best_oa_location":{"id":"pmh:oai:numdam.org:ITA_2014__48_4_467_0","is_oa":true,"landing_page_url":"http://www.numdam.org/articles/10.1051/ita/2014020/","pdf_url":"https://www.numdam.org/item/10.1051/ita/2014020.pdf","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1976449761.pdf","grobid_xml":"https://content.openalex.org/works/W1976449761.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W116841797","https://openalex.org/W1537696453","https://openalex.org/W1973714686","https://openalex.org/W1986142207","https://openalex.org/W1987875696","https://openalex.org/W2020326682","https://openalex.org/W2074547893","https://openalex.org/W2082354236","https://openalex.org/W2125915764","https://openalex.org/W2136069334","https://openalex.org/W2143943120","https://openalex.org/W2145467658","https://openalex.org/W2549921379"],"related_works":["https://openalex.org/W4226019574","https://openalex.org/W4306881917","https://openalex.org/W3212859878","https://openalex.org/W4286889508","https://openalex.org/W3210469369","https://openalex.org/W2120949095","https://openalex.org/W3102994322","https://openalex.org/W1930546149","https://openalex.org/W2945008796","https://openalex.org/W3190619779"],"abstract_inverted_index":{"A":[0],"k-abelian":[1,40],"cube":[2],"is":[3,54],"a":[4,45],"word":[5],"uvw,":[6],"where":[7],"the":[8,20],"factors":[9,28],"u,":[10],"v,":[11],"and":[12],"w":[13],"are":[14,42],"either":[15],"pairwise":[16],"equal,":[17],"or":[18],"have":[19],"same":[21],"multiplicities":[22],"for":[23,48,59],"every":[24],"one":[25],"of":[26,29],"their":[27],"length":[30],"at":[31],"most":[32],"k.":[33],"Previously":[34],"it":[35,53],"has":[36],"been":[37],"shown":[38],"that":[39,56],"cubes":[41],"avoidable":[43],"over":[44],"binary":[46],"alphabet":[47],"k":[49,60],"\u2265":[50,61],"8.":[51],"Here":[52],"proved":[55],"this":[57],"holds":[58],"5.":[62]},"counts_by_year":[{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":4}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}
