{"id":"https://openalex.org/W1985250725","doi":"https://doi.org/10.1142/s0218196708004597","title":"POLYNOMIAL CLONES ON SQUAREFREE GROUPS","display_name":"POLYNOMIAL CLONES ON SQUAREFREE GROUPS","publication_year":2008,"publication_date":"2008-06-01","ids":{"openalex":"https://openalex.org/W1985250725","doi":"https://doi.org/10.1142/s0218196708004597","mag":"1985250725"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196708004597","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196708004597","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/A5031760577","display_name":"Peter Mayr","orcid":"https://orcid.org/0000-0003-1163-313X"},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"PETER MAYR","raw_affiliation_strings":["Institut f\u00fcr Algebra, Johannes Kepler Universit\u00e4t Linz, 4040 Linz, Austria"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Algebra, Johannes Kepler Universit\u00e4t Linz, 4040 Linz, Austria","institution_ids":["https://openalex.org/I121883995"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5031760577"],"corresponding_institution_ids":["https://openalex.org/I121883995"],"apc_list":null,"apc_paid":null,"fwci":2.0557,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.83889062,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"18","issue":"04","first_page":"759","last_page":"777"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9987999796867371,"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":0.939368724822998},{"id":"https://openalex.org/keywords/square-free-integer","display_name":"Square-free integer","score":0.9225744009017944},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7051768898963928},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6955481171607971},{"id":"https://openalex.org/keywords/converse","display_name":"Converse","score":0.5151963829994202},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.453172504901886},{"id":"https://openalex.org/keywords/generating-set-of-a-group","display_name":"Generating set of a group","score":0.4462687075138092},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39320501685142517},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07225587964057922}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.939368724822998},{"id":"https://openalex.org/C188139237","wikidata":"https://www.wikidata.org/wiki/Q50706","display_name":"Square-free integer","level":2,"score":0.9225744009017944},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7051768898963928},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6955481171607971},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.5151963829994202},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.453172504901886},{"id":"https://openalex.org/C18116961","wikidata":"https://www.wikidata.org/wiki/Q734209","display_name":"Generating set of a group","level":2,"score":0.4462687075138092},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39320501685142517},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07225587964057922},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196708004597","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196708004597","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":7,"referenced_works":["https://openalex.org/W120124575","https://openalex.org/W1964770240","https://openalex.org/W2044212015","https://openalex.org/W2068117095","https://openalex.org/W3127823229","https://openalex.org/W4205325251","https://openalex.org/W4318826890"],"related_works":["https://openalex.org/W2387449261","https://openalex.org/W2418518962","https://openalex.org/W2963377682","https://openalex.org/W2043159103","https://openalex.org/W2391769344","https://openalex.org/W4297790016","https://openalex.org/W2359260952","https://openalex.org/W2769269860","https://openalex.org/W4362598163","https://openalex.org/W2388752733"],"abstract_inverted_index":{"We":[0,67],"prove":[1],"that,":[2,70],"on":[3],"a":[4,15,30,57,74,93],"set":[5],"of":[6,11,53,56,87],"size":[7],"n,":[8],"the":[9,38,47,50,80,84,88],"number":[10],"clones":[12],"that":[13,49],"contain":[14],"group":[16,59],"operation":[17,86],"and":[18,83],"all":[19],"constant":[20],"functions":[21],"is":[22,26,60,76],"finite":[23],"if":[24],"n":[25],"squarefree.":[27],"This":[28,91],"confirms":[29],"conjecture":[31,95],"by":[32,63,79],"Pawe\u0142":[33],"Idziak":[34],"from":[35,46,96],"[5]":[36],"where":[37],"converse":[39],"implication":[40],"was":[41],"shown.":[42],"Our":[43],"result":[44],"follows":[45],"observation":[48],"polynomial":[51],"clone":[52,75],"an":[54],"expansion":[55],"squarefree":[58],"uniquely":[61],"determined":[62,78],"its":[64],"binary":[65],"functions.":[66],"also":[68],"note":[69],"in":[71],"general,":[72],"such":[73],"not":[77],"congruence":[81],"lattice":[82],"commutator":[85],"corresponding":[89],"algebra.":[90],"refutes":[92],"second":[94],"[5].":[97]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
