{"id":"https://openalex.org/W4394992383","doi":"https://doi.org/10.1051/ita/2024011","title":"A Small Morphism for which the Fixed Point has an Abelian Critical Exponent Less than 2","display_name":"A Small Morphism for which the Fixed Point has an Abelian Critical Exponent Less than 2","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4394992383","doi":"https://doi.org/10.1051/ita/2024011"},"language":"en","primary_location":{"id":"doi:10.1051/ita/2024011","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ita/2024011","pdf_url":"https://www.rairo-ita.org/articles/ita/pdf/2024/01/ita230068.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":"hybrid","oa_url":"https://www.rairo-ita.org/articles/ita/pdf/2024/01/ita230068.pdf","any_repository_has_fulltext":false},"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":true,"raw_author_name":"James D. Currie","raw_affiliation_strings":["Department of Mathematics & Statistics, The University of Winnipeg, Winnipeg, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics & Statistics, The University of Winnipeg, Winnipeg, Canada","institution_ids":["https://openalex.org/I872945872"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023519726","display_name":"Narad Rampersad","orcid":"https://orcid.org/0000-0001-7489-0980"},"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":"Narad Rampersad","raw_affiliation_strings":["Department of Mathematics & Statistics, The University of Winnipeg, Winnipeg, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics & Statistics, The University of Winnipeg, Winnipeg, Canada","institution_ids":["https://openalex.org/I872945872"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5065770361"],"corresponding_institution_ids":["https://openalex.org/I872945872"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06500816,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"58","issue":null,"first_page":"14","last_page":"14"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9991999864578247,"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":0.9991999864578247,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9926000237464905,"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":0.9883999824523926,"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/morphism","display_name":"Morphism","score":0.8080551028251648},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.7226638793945312},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.6808757185935974},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6665306687355042},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.6046111583709717},{"id":"https://openalex.org/keywords/critical-exponent","display_name":"Critical exponent","score":0.4180791676044464},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39324963092803955},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22161084413528442},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13882678747177124}],"concepts":[{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.8080551028251648},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.7226638793945312},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.6808757185935974},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6665306687355042},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.6046111583709717},{"id":"https://openalex.org/C164154869","wikidata":"https://www.wikidata.org/wiki/Q901927","display_name":"Critical exponent","level":3,"score":0.4180791676044464},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39324963092803955},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22161084413528442},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13882678747177124},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1051/ita/2024011","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ita/2024011","pdf_url":"https://www.rairo-ita.org/articles/ita/pdf/2024/01/ita230068.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1051/ita/2024011","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ita/2024011","pdf_url":"https://www.rairo-ita.org/articles/ita/pdf/2024/01/ita230068.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education","score":0.5199999809265137}],"awards":[{"id":"https://openalex.org/G5472325981","display_name":null,"funder_award_id":"2019-04111","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G5585728123","display_name":null,"funder_award_id":"2017-03901","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4394992383.pdf"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1537696453","https://openalex.org/W1969770235","https://openalex.org/W1997246838","https://openalex.org/W2004336651","https://openalex.org/W2028370644","https://openalex.org/W2037721291","https://openalex.org/W2061829075","https://openalex.org/W2070037875","https://openalex.org/W2080123161","https://openalex.org/W2083930353","https://openalex.org/W2136069334","https://openalex.org/W2143943120","https://openalex.org/W2148206455","https://openalex.org/W2159956116","https://openalex.org/W3199914805","https://openalex.org/W4313316759"],"related_works":["https://openalex.org/W4390962471","https://openalex.org/W3106283477","https://openalex.org/W3127252294","https://openalex.org/W1970626112","https://openalex.org/W1975672403","https://openalex.org/W2559080656","https://openalex.org/W1963605683","https://openalex.org/W2091197480","https://openalex.org/W2016636497","https://openalex.org/W2054711049"],"abstract_inverted_index":{"It":[0],"is":[1],"known":[2],"that":[3],"there":[4],"are":[5],"infinite":[6],"words":[7],"over":[8,38],"finite":[9],"alphabets":[10],"with":[11],"Abelian":[12,49],"critical":[13,50],"exponent":[14,51],"arbitrarily":[15],"close":[16],"to":[17],"1;":[18],"however,":[19],"the":[20,44],"construction":[21],"previously":[22],"used":[23],"involves":[24],"huge":[25],"alphabets.":[26],"In":[27],"this":[28],"note":[29],"we":[30],"give":[31],"a":[32],"short":[33],"cyclic":[34],"morphism":[35],"(length":[36],"13)":[37],"an":[39,48],"8-letter":[40],"alphabet":[41],"for":[42],"which":[43],"fixed":[45],"point":[46],"has":[47],"less":[52],"than":[53],"1.8.":[54]},"counts_by_year":[],"updated_date":"2026-07-07T06:14:10.401900","created_date":"2025-10-10T00:00:00"}
