{"id":"https://openalex.org/W2003769565","doi":"https://doi.org/10.1142/s0129054112400680","title":"PERMUTATION COMPLEXITY AND THE LETTER DOUBLING MAP","display_name":"PERMUTATION COMPLEXITY AND THE LETTER DOUBLING MAP","publication_year":2012,"publication_date":"2012-12-01","ids":{"openalex":"https://openalex.org/W2003769565","doi":"https://doi.org/10.1142/s0129054112400680","mag":"2003769565"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054112400680","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054112400680","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"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 Foundations of Computer Science","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/A5020118331","display_name":"Steven Widmer","orcid":null},"institutions":[{"id":"https://openalex.org/I123534392","display_name":"University of North Texas","ror":"https://ror.org/00v97ad02","country_code":"US","type":"education","lineage":["https://openalex.org/I123534392"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"STEVEN WIDMER","raw_affiliation_strings":["Mathematics Department, University of North Texas, Denton, Texas 76203, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, University of North Texas, Denton, Texas 76203, USA","institution_ids":["https://openalex.org/I123534392"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5020118331"],"corresponding_institution_ids":["https://openalex.org/I123534392"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.09046047,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"23","issue":"08","first_page":"1653","last_page":"1675"},"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/T12029","display_name":"DNA and Biological Computing","score":0.9915000200271606,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9897000193595886,"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/countable-set","display_name":"Countable set","score":0.7853918671607971},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7652998566627502},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.7594996690750122},{"id":"https://openalex.org/keywords/aperiodic-graph","display_name":"Aperiodic graph","score":0.7349264621734619},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7030857801437378},{"id":"https://openalex.org/keywords/cyclic-permutation","display_name":"Cyclic permutation","score":0.6253138780593872},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5333729982376099},{"id":"https://openalex.org/keywords/partial-permutation","display_name":"Partial permutation","score":0.5164020657539368},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5102968215942383},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.5051453709602356},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5014114379882812},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4391304552555084},{"id":"https://openalex.org/keywords/derangement","display_name":"Derangement","score":0.42816174030303955},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4254639744758606},{"id":"https://openalex.org/keywords/bit-reversal-permutation","display_name":"Bit-reversal permutation","score":0.42101263999938965},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.14608651399612427},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1317516267299652},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.12934449315071106}],"concepts":[{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.7853918671607971},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7652998566627502},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.7594996690750122},{"id":"https://openalex.org/C104247578","wikidata":"https://www.wikidata.org/wiki/Q4779368","display_name":"Aperiodic graph","level":2,"score":0.7349264621734619},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7030857801437378},{"id":"https://openalex.org/C77670614","wikidata":"https://www.wikidata.org/wiki/Q212130","display_name":"Cyclic permutation","level":3,"score":0.6253138780593872},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5333729982376099},{"id":"https://openalex.org/C145633696","wikidata":"https://www.wikidata.org/wiki/Q1401935","display_name":"Partial permutation","level":4,"score":0.5164020657539368},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5102968215942383},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.5051453709602356},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5014114379882812},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4391304552555084},{"id":"https://openalex.org/C38298161","wikidata":"https://www.wikidata.org/wiki/Q1207920","display_name":"Derangement","level":2,"score":0.42816174030303955},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4254639744758606},{"id":"https://openalex.org/C175473596","wikidata":"https://www.wikidata.org/wiki/Q4918660","display_name":"Bit-reversal permutation","level":4,"score":0.42101263999938965},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.14608651399612427},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1317516267299652},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.12934449315071106},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0129054112400680","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054112400680","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"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 Foundations of Computer Science","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":9,"referenced_works":["https://openalex.org/W1574079735","https://openalex.org/W1963909585","https://openalex.org/W1968553864","https://openalex.org/W2006431506","https://openalex.org/W2010637097","https://openalex.org/W2015622212","https://openalex.org/W2037993261","https://openalex.org/W2061248690","https://openalex.org/W4244795967"],"related_works":["https://openalex.org/W4383755479","https://openalex.org/W2363611940","https://openalex.org/W2385551783","https://openalex.org/W1997601808","https://openalex.org/W2125494331","https://openalex.org/W2964309395","https://openalex.org/W4243765674","https://openalex.org/W2613407656","https://openalex.org/W4302067876","https://openalex.org/W4285292213"],"abstract_inverted_index":{"Given":[0],"a":[1,19,67],"countable":[2],"set":[3],"X":[4,17],"(usually":[5],"taken":[6],"to":[7],"be":[8],"\u2115":[9,39],"or":[10],"\u2124),":[11],"an":[12],"infinite":[13,36],"permutation":[14],"\u03c0":[15,23],"of":[16,24,35,44],"is":[18,61,72],"linear":[20],"ordering":[21],"\u227a":[22],"X,":[25],"introduced":[26],"in":[27],"[6].":[28],"This":[29],"paper":[30],"investigates":[31],"the":[32,42,51,59,70,75,79],"combinatorial":[33],"complexity":[34,60,71],"permutations":[37],"on":[38],"associated":[40],"with":[41],"image":[43],"uniformly":[45],"recurrent":[46],"aperiodic":[47],"binary":[48],"words":[49,77],"under":[50],"letter":[52],"doubling":[53],"map.":[54],"An":[55],"upper":[56],"bound":[57],"for":[58,63,69,74],"found":[62],"general":[64],"words,":[65],"and":[66,78],"formula":[68],"established":[73],"Sturmian":[76],"Thue-Morse":[80],"word.":[81]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}