{"id":"https://openalex.org/W1925759471","doi":"https://doi.org/10.37236/974","title":"Shape-Wilf-Ordering on Permutations of Length 3","display_name":"Shape-Wilf-Ordering on Permutations of Length 3","publication_year":2007,"publication_date":"2007-08-20","ids":{"openalex":"https://openalex.org/W1925759471","doi":"https://doi.org/10.37236/974","mag":"1925759471"},"language":"en","primary_location":{"id":"doi:10.37236/974","is_oa":true,"landing_page_url":"https://doi.org/10.37236/974","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r56/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r56/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068759323","display_name":"Zvezdelina Stankova","orcid":null},"institutions":[{"id":"https://openalex.org/I91481961","display_name":"Mills College","ror":"https://ror.org/01ynb8e46","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129","https://openalex.org/I91481961"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Zvezdelina Stankova","raw_affiliation_strings":["Dept. of Mathematics and Computer Science Mills College, Oakland, California, USA"],"affiliations":[{"raw_affiliation_string":"Dept. of Mathematics and Computer Science Mills College, Oakland, California, USA","institution_ids":["https://openalex.org/I91481961"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5068759323"],"corresponding_institution_ids":["https://openalex.org/I91481961"],"apc_list":null,"apc_paid":null,"fwci":0.5251,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.57692308,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"14","issue":"1","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/T11567","display_name":"semigroups and automata theory","score":0.9965999722480774,"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/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9847999811172485,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8086321353912354},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7725355625152588},{"id":"https://openalex.org/keywords/fibonacci-number","display_name":"Fibonacci number","score":0.6954382658004761},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6167593002319336},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5892224907875061},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5468929409980774},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.4632478952407837},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.44569987058639526},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19762343168258667},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09802195429801941}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8086321353912354},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7725355625152588},{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.6954382658004761},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6167593002319336},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5892224907875061},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5468929409980774},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.4632478952407837},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.44569987058639526},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19762343168258667},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09802195429801941},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/974","is_oa":true,"landing_page_url":"https://doi.org/10.37236/974","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r56/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/974","is_oa":true,"landing_page_url":"https://doi.org/10.37236/974","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r56/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1925759471.pdf","grobid_xml":"https://content.openalex.org/works/W1925759471.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1500943703","https://openalex.org/W1984841421","https://openalex.org/W1992104349","https://openalex.org/W2015106956","https://openalex.org/W2029005417","https://openalex.org/W2038250522","https://openalex.org/W2043773469","https://openalex.org/W2047160913","https://openalex.org/W2048313572","https://openalex.org/W2050039992","https://openalex.org/W2091015960","https://openalex.org/W2105493981","https://openalex.org/W2129036921","https://openalex.org/W2143645603","https://openalex.org/W2167602228","https://openalex.org/W2168316830","https://openalex.org/W2752061190","https://openalex.org/W2752853835","https://openalex.org/W2912910446","https://openalex.org/W2950382558","https://openalex.org/W2999007559","https://openalex.org/W3103273172","https://openalex.org/W4212838771","https://openalex.org/W4235551663","https://openalex.org/W4237930722","https://openalex.org/W4253748139","https://openalex.org/W6605093462","https://openalex.org/W6633749307"],"related_works":["https://openalex.org/W2920386017","https://openalex.org/W2795454383","https://openalex.org/W4317662907","https://openalex.org/W2054041134","https://openalex.org/W1965364641","https://openalex.org/W4316467349","https://openalex.org/W2896847511","https://openalex.org/W2313406248","https://openalex.org/W2007817959","https://openalex.org/W2241227810"],"abstract_inverted_index":{"The":[0,14],"research":[1],"on":[2,10,46],"pattern-avoidance":[3,187],"has":[4,33],"yielded":[5],"so":[6],"far":[7],"limited":[8],"knowledge":[9],"Wilf-ordering":[11],"of":[12,26,43,49,74,170,173,178,185],"permutations.":[13,137],"Stanley-Wilf":[15],"limits":[16],"$\\lim_{n\\rightarrow":[17],"\\infty}":[18],"\\sqrt[n]{|S_n(\\tau)|}$":[19],"and":[20,105,130,156],"further":[21],"works":[22],"suggest":[23],"asymptotic":[24],"ordering":[25,48,78],"layered":[27],"versus":[28],"monotone":[29],"patterns.":[30],"Yet,":[31],"B\u00f3na":[32],"provided":[34],"essentially":[35],"the":[36,82,151,168,182],"only":[37],"known":[38],"up":[39,80,167],"to":[40,81,134,148],"now":[41],"result":[42,76,133],"its":[44],"type":[45],"complete":[47],"$S_k$":[50],"for":[51,58,88,101,114],"$k=4$:":[52],"$|S_n(1342)|":[53],"&lt;":[54,56],"|S_n(1234)|":[55],"|S_n(1324)|$":[57],"$n\\geq":[59],"7$,":[60],"along":[61],"with":[62,123],"some":[63,176],"other":[64,125],"sporadic":[65],"examples":[66],"in":[67,145],"Wilf-ordering.":[68],"We":[69],"give":[70],"a":[71,95],"different":[72],"proof":[73],"this":[75],"by":[77,160],"$S_3$":[79],"stronger":[83],"shape-Wilf-order:":[84],"$|S_Y(213)|\\leq":[85],"|S_Y(123)|\\leq":[86],"|S_Y(312)|$":[87],"any":[89,102],"Young":[90,163],"diagram":[91],"$Y$,":[92],"derive":[93],"as":[94],"consequence":[96],"that":[97,120],"$|S_Y(k+2,k+1,k+3,\\tau)|\\leq":[98],"|S_Y(k+1,k+2,k+3,\\tau)|\\leq":[99],"|S_Y(k+3,k+1,k+2,\\tau)|$":[100],"$\\tau\\in":[103],"S_k$,":[104],"find":[106,118],"out":[107,119],"when":[108],"equalities":[109],"are":[110],"obtained.":[111],"(In":[112],"particular,":[113],"specific":[115],"$Y$'s":[116],"we":[117],"$|S_Y(123)|=|S_Y(312)|$":[121],"coincide":[122],"every":[124],"Fibonacci":[126],"term.)":[127],"This":[128,165],"strengthens":[129],"generalizes":[131],"B\u00f3na's":[132],"arbitrary":[135],"length":[136],"While":[138],"all":[139,162],"length-3":[140],"permutations":[141,159],"have":[142],"been":[143],"shown":[144],"numerous":[146],"ways":[147],"be":[149],"Wilf-equivalent,":[150],"current":[152],"paper":[153],"distinguishes":[154],"between":[155],"orders":[157],"these":[158],"employing":[161],"diagrams.":[164],"opens":[166],"question":[169],"whether":[171],"shape-Wilf-ordering":[172],"permutations,":[174],"or":[175],"generalization":[177],"it,":[179],"is":[180],"not":[181],"\"true\"":[183],"way":[184],"approaching":[186],"ordering.":[188]},"counts_by_year":[{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
