{"id":"https://openalex.org/W2153752510","doi":"https://doi.org/10.37236/4119","title":"Operators of Equivalent Sorting Power and Related Wilf-equivalences","display_name":"Operators of Equivalent Sorting Power and Related Wilf-equivalences","publication_year":2014,"publication_date":"2014-10-09","ids":{"openalex":"https://openalex.org/W2153752510","doi":"https://doi.org/10.37236/4119","mag":"2153752510"},"language":"en","primary_location":{"id":"doi:10.37236/4119","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4119","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i4p11/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i4p11/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001631971","display_name":"Michael Albert","orcid":"https://orcid.org/0009-0006-0659-7743"},"institutions":[{"id":"https://openalex.org/I80281795","display_name":"University of Otago","ror":"https://ror.org/01jmxt844","country_code":"NZ","type":"education","lineage":["https://openalex.org/I80281795"]}],"countries":["NZ"],"is_corresponding":true,"raw_author_name":"Michael Albert","raw_affiliation_strings":["Department of Computer Science \r\nUniversity of Otago \r\nDunedin, New Zealand"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science \r\nUniversity of Otago \r\nDunedin, New Zealand","institution_ids":["https://openalex.org/I80281795"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110181824","display_name":"Mathilde Bouvel","orcid":null},"institutions":[{"id":"https://openalex.org/I202697423","display_name":"University of Zurich","ror":"https://ror.org/02crff812","country_code":"CH","type":"education","lineage":["https://openalex.org/I202697423"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Mathilde Bouvel","raw_affiliation_strings":["Institut f\u00fcr Mathematik \r\nUniversit\u00e4t Z\u00fcrich \r\nZ\u00fcrich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik \r\nUniversit\u00e4t Z\u00fcrich \r\nZ\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I202697423"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5001631971"],"corresponding_institution_ids":["https://openalex.org/I80281795"],"apc_list":null,"apc_paid":null,"fwci":1.6416,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.82188145,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"21","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998000264167786,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998000264167786,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9933000206947327,"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/bijection","display_name":"Bijection","score":0.9726393222808838},{"id":"https://openalex.org/keywords/bijection-injection-and-surjection","display_name":"Bijection, injection and surjection","score":0.9489421844482422},{"id":"https://openalex.org/keywords/equidistributed-sequence","display_name":"Equidistributed sequence","score":0.926875650882721},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.8372973203659058},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7629851698875427},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.753387987613678},{"id":"https://openalex.org/keywords/sorting","display_name":"Sorting","score":0.6405800580978394},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.555677056312561},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5105654001235962},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44420191645622253},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4282992482185364},{"id":"https://openalex.org/keywords/power-set","display_name":"Power set","score":0.42714256048202515},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14713197946548462},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08061632513999939},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07448732852935791}],"concepts":[{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.9726393222808838},{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.9489421844482422},{"id":"https://openalex.org/C50742451","wikidata":"https://www.wikidata.org/wiki/Q1530388","display_name":"Equidistributed sequence","level":2,"score":0.926875650882721},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.8372973203659058},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7629851698875427},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.753387987613678},{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.6405800580978394},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.555677056312561},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5105654001235962},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44420191645622253},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4282992482185364},{"id":"https://openalex.org/C100643331","wikidata":"https://www.wikidata.org/wiki/Q205170","display_name":"Power set","level":3,"score":0.42714256048202515},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14713197946548462},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08061632513999939},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07448732852935791},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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":2,"locations":[{"id":"doi:10.37236/4119","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4119","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i4p11/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1402.2034","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1402.2034","pdf_url":"https://arxiv.org/pdf/1402.2034","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":{"id":"doi:10.37236/4119","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4119","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i4p11/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4160044894","display_name":null,"funder_award_id":"151254","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2153752510.pdf","grobid_xml":"https://content.openalex.org/works/W2153752510.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W116277488","https://openalex.org/W166539567","https://openalex.org/W1538027092","https://openalex.org/W1576215713","https://openalex.org/W1627704219","https://openalex.org/W1980065683","https://openalex.org/W1981803420","https://openalex.org/W2006800405","https://openalex.org/W2012267021","https://openalex.org/W2017788080","https://openalex.org/W2027678923","https://openalex.org/W2074370694","https://openalex.org/W2077866342","https://openalex.org/W2083354900","https://openalex.org/W2113209621","https://openalex.org/W2153752510","https://openalex.org/W2160566290","https://openalex.org/W2172232275","https://openalex.org/W2752061190","https://openalex.org/W2752853835","https://openalex.org/W4212838771","https://openalex.org/W4300773925","https://openalex.org/W7007771209"],"related_works":["https://openalex.org/W2952259524","https://openalex.org/W2160566290","https://openalex.org/W2806276129","https://openalex.org/W2021895108","https://openalex.org/W2153752510","https://openalex.org/W2602388795","https://openalex.org/W2952981421","https://openalex.org/W4213409680","https://openalex.org/W4313441736","https://openalex.org/W2949947309"],"abstract_inverted_index":{"We":[0,114],"study":[1],"sorting":[2,13],"operators":[3],"$\\mathbf{A}$":[4],"on":[5,90],"permutations":[6,40,97],"that":[7,59,70],"are":[8,62,75],"obtained":[9],"composing":[10],"Knuth's":[11],"stack":[12],"operator":[14,19,29],"$\\mathbf{S}$":[15],"and":[16,46,102],"the":[17,37,47,65,94,99,103],"reversal":[18],"$\\mathbf{R}$,":[20],"as":[21,24],"many":[22,71,111],"times":[23],"desired.":[25],"For":[26],"any":[27],"such":[28],"$\\mathbf{A}$,":[30],"we":[31],"provide":[32],"a":[33,91],"size-preserving":[34],"bijection":[35,92],"between":[36,93],"set":[38,48,95,104],"of":[39,49,83,86,96,105,119,127],"sorted":[41,51],"by":[42,52,64],"$\\mathbf{S}":[43,53],"\\circ":[44,54,56],"\\mathbf{A}$":[45],"those":[50,106],"\\mathbf{R}":[55],"\\mathbf{A}$,":[57],"proving":[58],"these":[60,78],"sets":[61],"enumerated":[63],"same":[66],"sequence,":[67],"but":[68],"also":[69,115],"classical":[72],"permutation":[73,112,129],"statistics":[74],"equidistributed":[76],"across":[77],"two":[79],"sets.":[80],"The":[81],"description":[82],"this":[84,120],"family":[85],"bijections":[87],"is":[88],"based":[89],"avoiding":[98,107],"pattern":[100],"$231$":[101],"$132$":[108],"which":[109],"preserves":[110],"statistics.":[113],"present":[116],"other":[117],"properties":[118],"bijection,":[121],"in":[122],"particular":[123],"for":[124],"finding":[125],"pairs":[126],"Wilf-equivalent":[128],"classes.":[130]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
