{"id":"https://openalex.org/W2045720037","doi":"https://doi.org/10.1142/s0218196709005457","title":"CODING PARTITIONS OF REGULAR SETS","display_name":"CODING PARTITIONS OF REGULAR SETS","publication_year":2009,"publication_date":"2009-12-01","ids":{"openalex":"https://openalex.org/W2045720037","doi":"https://doi.org/10.1142/s0218196709005457","mag":"2045720037"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196709005457","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196709005457","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/A5019936163","display_name":"Marie-Pierre B\u00e9al","orcid":"https://orcid.org/0000-0002-0089-1486"},"institutions":[{"id":"https://openalex.org/I4210152518","display_name":"Laboratoire d'Informatique Gaspard-Monge","ror":"https://ror.org/04t50yk91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210145102","https://openalex.org/I4210152518","https://openalex.org/I4210154111","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"MARIE-PIERRE B\u00c9AL","raw_affiliation_strings":["Universit\u00e9 Paris-Est, Laboratoire d'informatique Gaspard-Monge, CNRS, 77454 Marne-la-Vall\u00e9e Cedex 2, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris-Est, Laboratoire d'informatique Gaspard-Monge, CNRS, 77454 Marne-la-Vall\u00e9e Cedex 2, France","institution_ids":["https://openalex.org/I4210152518","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061378490","display_name":"Fabio Burderi","orcid":"https://orcid.org/0000-0002-1380-867X"},"institutions":[{"id":"https://openalex.org/I900890020","display_name":"University of Palermo","ror":"https://ror.org/044k9ta02","country_code":"IT","type":"education","lineage":["https://openalex.org/I900890020"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"FABIO BURDERI","raw_affiliation_strings":["Dipartimento di Matematica ed Applicazioni, Universit\u00e0 degli studi di Palermo, Via Archirafi 34, 90123 Palermo, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica ed Applicazioni, Universit\u00e0 degli studi di Palermo, Via Archirafi 34, 90123 Palermo, Italy","institution_ids":["https://openalex.org/I900890020"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024448520","display_name":"Antonio Restivo","orcid":"https://orcid.org/0000-0002-1972-6931"},"institutions":[{"id":"https://openalex.org/I900890020","display_name":"University of Palermo","ror":"https://ror.org/044k9ta02","country_code":"IT","type":"education","lineage":["https://openalex.org/I900890020"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"ANTONIO RESTIVO","raw_affiliation_strings":["Dipartimento di Matematica ed Applicazioni, Universit\u00e0 degli studi di Palermo, Via Archirafi 34, 90123 Palermo, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica ed Applicazioni, Universit\u00e0 degli studi di Palermo, Via Archirafi 34, 90123 Palermo, Italy","institution_ids":["https://openalex.org/I900890020"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5019936163"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210152518"],"apc_list":null,"apc_paid":null,"fwci":0.709,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.7125192,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"19","issue":"08","first_page":"1011","last_page":"1023"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9969000220298767,"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":0.9940000176429749,"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/mathematics","display_name":"Mathematics","score":0.8504816293716431},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6951745748519897},{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.6520615816116333},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.5648086071014404},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48402756452560425},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4771116077899933}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8504816293716431},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6951745748519897},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.6520615816116333},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.5648086071014404},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48402756452560425},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4771116077899933},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218196709005457","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196709005457","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"},{"id":"pmh:oai:HAL:hal-00826118v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00826118","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Algebra and Computation, 2009, 19 (8), pp.1011-1023. ⟨10.1142/S0218196709005457⟩","raw_type":"Journal articles"},{"id":"pmh:oai:iris.unipa.it:10447/45816","is_oa":false,"landing_page_url":"http://hdl.handle.net/10447/45816","pdf_url":null,"source":{"id":"https://openalex.org/S4306401065","display_name":"Nova Science Publishers (Nova Science Publishers, Inc.)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W26034628","https://openalex.org/W196919032","https://openalex.org/W585175573","https://openalex.org/W1584451387","https://openalex.org/W1984800684","https://openalex.org/W1995652642","https://openalex.org/W2049048592","https://openalex.org/W2071754338","https://openalex.org/W2072847621","https://openalex.org/W2074969379","https://openalex.org/W2099899183","https://openalex.org/W2132750992","https://openalex.org/W2167954650","https://openalex.org/W2798988860","https://openalex.org/W2913344232","https://openalex.org/W4206635485","https://openalex.org/W4301343535","https://openalex.org/W4302394292","https://openalex.org/W6663007966"],"related_works":["https://openalex.org/W3161268522","https://openalex.org/W3130993066","https://openalex.org/W2544600950","https://openalex.org/W2120366296","https://openalex.org/W2386248435","https://openalex.org/W2950820214","https://openalex.org/W2005979015","https://openalex.org/W1128915060","https://openalex.org/W3023741988","https://openalex.org/W2145532887"],"abstract_inverted_index":{"A":[0],"coding":[1,37,42,74],"partition":[2,38,43,75],"of":[3,6,18,27,48,66,76,84,103,111],"a":[4,16,77,81,100,104,108],"set":[5,10,47,79],"words":[7,26,49],"partitions":[8,45],"this":[9,94,97],"into":[11,107],"classes":[12,58,86],"such":[13],"that":[14,44,59,71],"whenever":[15],"sequence,":[17],"minimal":[19],"length,":[20],"has":[21],"two":[22],"distinct":[23],"factorizations,":[24],"the":[25,32,40,46,61,64,72],"these":[28],"factorizations":[29,65],"belong":[30],"to":[31],"same":[33],"class.":[34],"The":[35],"canonical":[36,73,101],"is":[39],"finest":[41],"in":[50,63],"at":[51],"most":[52],"one":[53],"unambiguous":[54],"class":[55],"and":[56,87],"other":[57],"localize":[60],"ambiguities":[62],"finite":[67,82],"sequences.":[68],"We":[69],"prove":[70],"regular":[78,85,105,114],"contains":[80],"number":[83],"we":[88,98],"give":[89],"an":[90],"algorithm":[91],"for":[92],"computing":[93],"partition.":[95],"From":[96],"derive":[99],"decomposition":[102],"monoid":[106],"free":[109],"product":[110],"finitely":[112],"many":[113],"monoids.":[115]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}