{"id":"https://openalex.org/W2074662282","doi":"https://doi.org/10.2178/jsl/1327068698","title":"Normal forms for elementary patterns","display_name":"Normal forms for elementary patterns","publication_year":2012,"publication_date":"2012-01-20","ids":{"openalex":"https://openalex.org/W2074662282","doi":"https://doi.org/10.2178/jsl/1327068698","mag":"2074662282"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1327068698","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1327068698","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Symbolic Logic","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/A5112868263","display_name":"Timothy J. Carlson","orcid":null},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Timothy J. Carlson","raw_affiliation_strings":["Department of Mathematics, The Ohio State University, 231 W 18th Avenue, Columbus, OH 43210, USA, E-mail:","Department of Mathematics, The Ohio State University, 231 W 18th Avenue, Columbus, OH 43210, USA, E-mail: carlson@math.ohio-state.edu"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Ohio State University, 231 W 18th Avenue, Columbus, OH 43210, USA, E-mail:","institution_ids":["https://openalex.org/I52357470"]},{"raw_affiliation_string":"Department of Mathematics, The Ohio State University, 231 W 18th Avenue, Columbus, OH 43210, USA, E-mail: carlson@math.ohio-state.edu","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019535832","display_name":"Gunnar Wilken","orcid":"https://orcid.org/0000-0002-4019-9320"},"institutions":[{"id":"https://openalex.org/I142637625","display_name":"Okinawa Institute of Science and Technology Graduate University","ror":"https://ror.org/02qg15b79","country_code":"JP","type":"education","lineage":["https://openalex.org/I142637625"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Gunnar Wilken","raw_affiliation_strings":["Mathematical Biology Unit, Okinawa Institute of Science and Technology, 1919-1 Tancha, Onna-Son, 904-0412 Okinawa, Japan, E-mail:","Mathematical Biology Unit, Okinawa Institute of Science and Technology, 1919-1 Tancha, Onna-Son, 904-0412 Okinawa, Japan, E-mail: wilken@oist.jp"],"affiliations":[{"raw_affiliation_string":"Mathematical Biology Unit, Okinawa Institute of Science and Technology, 1919-1 Tancha, Onna-Son, 904-0412 Okinawa, Japan, E-mail:","institution_ids":["https://openalex.org/I142637625"]},{"raw_affiliation_string":"Mathematical Biology Unit, Okinawa Institute of Science and Technology, 1919-1 Tancha, Onna-Son, 904-0412 Okinawa, Japan, E-mail: wilken@oist.jp","institution_ids":["https://openalex.org/I142637625"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5112868263"],"corresponding_institution_ids":["https://openalex.org/I52357470"],"apc_list":null,"apc_paid":null,"fwci":0.3369,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.6216763,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"77","issue":"1","first_page":"174","last_page":"194"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9745000004768372,"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":0.9745000004768372,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9469000101089478,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.8218801021575928},{"id":"https://openalex.org/keywords/arithmetic-function","display_name":"Arithmetic function","score":0.6117215752601624},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5930261611938477},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5571987628936768},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5397892594337463},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5310754179954529},{"id":"https://openalex.org/keywords/meaning","display_name":"Meaning (existential)","score":0.4741002023220062},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44199734926223755},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3631983697414398},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2812066674232483},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.24294346570968628},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19305971264839172},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.16708019375801086},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.04970642924308777}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.8218801021575928},{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.6117215752601624},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5930261611938477},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5571987628936768},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5397892594337463},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5310754179954529},{"id":"https://openalex.org/C2780876879","wikidata":"https://www.wikidata.org/wiki/Q3054749","display_name":"Meaning (existential)","level":2,"score":0.4741002023220062},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44199734926223755},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3631983697414398},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2812066674232483},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.24294346570968628},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19305971264839172},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.16708019375801086},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.04970642924308777},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/jsl/1327068698","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1327068698","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1327068698","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1327068698","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.6899999976158142}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1987053402","https://openalex.org/W2018457617","https://openalex.org/W2031449549","https://openalex.org/W2032474274","https://openalex.org/W2081882471","https://openalex.org/W2094980193","https://openalex.org/W2115737962"],"related_works":["https://openalex.org/W2000071592","https://openalex.org/W1660676450","https://openalex.org/W1586473494","https://openalex.org/W2382181079","https://openalex.org/W2125955092","https://openalex.org/W2119550093","https://openalex.org/W582971654","https://openalex.org/W2861978802","https://openalex.org/W1989539286","https://openalex.org/W4252643736"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"notation":[2,61],"for":[3,27,108,115],"an":[4,14,55],"ordinal":[5,99],"using":[6,75,95],"patterns":[7,116,132],"of":[8,17,58,71,98,112,117,130,133],"resemblance":[9],"is":[10,46,49],"based":[11,78],"on":[12,79],"choosing":[13],"isominimal":[15,43,73],"set":[16,29,74],"ordinals":[18],"containing":[19],"the":[20,69,87,127],"given":[21],"ordinal.":[22],"There":[23],"are":[24,33],"many":[25],"choices":[26],"this":[28,63,72],"meaning":[30],"that":[31,39],"notations":[32,77],"far":[34],"from":[35],"unique.":[36],"We":[37],"establish":[38],"among":[40],"all":[41],"such":[42],"sets":[44],"there":[45],"one":[47,119],"which":[48,104],"smallest":[50],"under":[51],"inclusion":[52],"thus":[53],"providing":[54],"appropriate":[56],"notion":[57],"normal":[59,113],"form":[60],"in":[62,89,102,126],"context.":[64],"In":[65],"addition,":[66],"we":[67],"calculate":[68],"elements":[70],"standard":[76],"collapsing":[80],"functions.":[81],"This":[82],"provides":[83],"a":[84,109,123],"capstone":[85],"to":[86],"results":[88],"[2,":[90],"6,":[91],"8,":[92],"9,":[93],"7],":[94],"further":[96],"refinement":[97],"arithmetic":[100],"developed":[101],"[8]":[103],"then":[105],"both":[106],"allows":[107],"simple":[110],"characterization":[111],"forms":[114],"order":[118,134],"and":[120],"will":[121],"play":[122],"key":[124],"role":[125],"arithmetical":[128],"analysis":[129],"pure":[131],"two,":[135],"[5].":[136]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}