{"id":"https://openalex.org/W2042321150","doi":"https://doi.org/10.1142/s0218196709005378","title":"ON THE CAYLEY SEMIGROUP OF A FINITE APERIODIC SEMIGROUP","display_name":"ON THE CAYLEY SEMIGROUP OF A FINITE APERIODIC SEMIGROUP","publication_year":2009,"publication_date":"2009-09-01","ids":{"openalex":"https://openalex.org/W2042321150","doi":"https://doi.org/10.1142/s0218196709005378","mag":"2042321150"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196709005378","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196709005378","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/A5086263195","display_name":"Avi I. Mintz","orcid":"https://orcid.org/0000-0002-2995-1868"},"institutions":[{"id":"https://openalex.org/I13955877","display_name":"Bar-Ilan University","ror":"https://ror.org/03kgsv495","country_code":"IL","type":"education","lineage":["https://openalex.org/I13955877"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"AVI MINTZ","raw_affiliation_strings":["Bar-Ilan University, Ramat Gan 52900, Israel","Bar-Ilan University Ramat-Gan, 52900 Israel,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bar-Ilan University, Ramat Gan 52900, Israel","institution_ids":["https://openalex.org/I13955877"]},{"raw_affiliation_string":"Bar-Ilan University Ramat-Gan, 52900 Israel,","institution_ids":["https://openalex.org/I13955877"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5086263195"],"corresponding_institution_ids":["https://openalex.org/I13955877"],"apc_list":null,"apc_paid":null,"fwci":0.3545,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.61576865,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"19","issue":"06","first_page":"723","last_page":"746"},"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9937999844551086,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/aperiodic-graph","display_name":"Aperiodic graph","score":0.9581890106201172},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8898280262947083},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.8658972382545471},{"id":"https://openalex.org/keywords/cancellative-semigroup","display_name":"Cancellative semigroup","score":0.7067696452140808},{"id":"https://openalex.org/keywords/bicyclic-semigroup","display_name":"Bicyclic semigroup","score":0.669136643409729},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.45096710324287415},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4005192220211029},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.30848151445388794}],"concepts":[{"id":"https://openalex.org/C104247578","wikidata":"https://www.wikidata.org/wiki/Q4779368","display_name":"Aperiodic graph","level":2,"score":0.9581890106201172},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8898280262947083},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.8658972382545471},{"id":"https://openalex.org/C21112865","wikidata":"https://www.wikidata.org/wiki/Q5031372","display_name":"Cancellative semigroup","level":3,"score":0.7067696452140808},{"id":"https://openalex.org/C40417594","wikidata":"https://www.wikidata.org/wiki/Q3022111","display_name":"Bicyclic semigroup","level":3,"score":0.669136643409729},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45096710324287415},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4005192220211029},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30848151445388794}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196709005378","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196709005378","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1581663038","https://openalex.org/W1585649433","https://openalex.org/W2001772188","https://openalex.org/W2020235161","https://openalex.org/W2036018689","https://openalex.org/W3216142546"],"related_works":["https://openalex.org/W2023293387","https://openalex.org/W4243399255","https://openalex.org/W114852214","https://openalex.org/W2107948742","https://openalex.org/W2387049078","https://openalex.org/W2388317430","https://openalex.org/W2465992524","https://openalex.org/W3187473336","https://openalex.org/W2319463501","https://openalex.org/W2951456742"],"abstract_inverted_index":{"Let":[0],"S":[1,52,70],"be":[2],"a":[3,38,42,45,54],"finite":[4,55,72],"semigroup.":[5],"In":[6],"this":[7],"paper,":[8],"we":[9],"introduce":[10],"the":[11,59,63],"functions":[12,64],"\u03c6":[13,24],"s":[14,25,66,68],":S*":[15],"\u2192":[16],"S*,":[17],"first":[18],"defined":[19],"by":[20,23,62],"Rhodes,":[21],"given":[22],"([a":[26],"1":[27,35,37,41],",a":[28],"2":[29,39,43],",\u2026,a":[30],"n":[31,46],"])":[32],"=":[33],"[sa":[34],",sa":[36],",\u2026,sa":[40],"\u22ef":[44],"].":[47],"We":[48],"show":[49],"that":[50],"if":[51],"is":[53,71],"aperiodic":[56],"semigroup,":[57],"then":[58],"semigroup":[60],"generated":[61],"{\u03c6":[65],"}":[67],"\u2208":[69],"and":[73],"aperiodic.":[74]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2025-10-10T00:00:00"}
