{"id":"https://openalex.org/W2999007559","doi":"https://doi.org/10.37236/1477","title":"On the Stanley-Wilf Conjecture for the Number of Permutations Avoiding a Given Pattern","display_name":"On the Stanley-Wilf Conjecture for the Number of Permutations Avoiding a Given Pattern","publication_year":1999,"publication_date":"1999-08-25","ids":{"openalex":"https://openalex.org/W2999007559","doi":"https://doi.org/10.37236/1477","mag":"2999007559"},"language":"en","primary_location":{"id":"doi:10.37236/1477","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1477","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v6i1n1/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":false,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v6i1n1/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060984153","display_name":"Richard Arratia","orcid":null},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Richard Arratia","raw_affiliation_strings":["Department of Mathematics University of Southern California Los Angeles , CA 90089-1113","Department of Mathematics University of Southern California Los Angeles, CA 90089-1113"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Southern California Los Angeles , CA 90089-1113","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"Department of Mathematics University of Southern California Los Angeles, CA 90089-1113","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5060984153"],"corresponding_institution_ids":["https://openalex.org/I1174212"],"apc_list":null,"apc_paid":null,"fwci":1.7679,"has_fulltext":true,"cited_by_count":124,"citation_normalized_percentile":{"value":0.85967399,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"6","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":0.9994999766349792,"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":0.9994999766349792,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9921000003814697,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9894000291824341,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8742325305938721},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.8732212781906128},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8364316821098328},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.7526336312294006},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.5838851928710938},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4940186142921448},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37678951025009155},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09757211804389954}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8742325305938721},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8732212781906128},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8364316821098328},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.7526336312294006},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.5838851928710938},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4940186142921448},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37678951025009155},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09757211804389954},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/1477","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1477","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v6i1n1/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":false,"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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.43.3387","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.43.3387","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cirm.univ-mrs.fr/EMIS/journals/EJC/Volume_6/PostScriptfiles/v6i1n1.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.45.9796","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.9796","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_6/../Volume_6/PostScriptfiles/v6i1n1.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1477","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1477","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v6i1n1/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":false,"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/W2999007559.pdf","grobid_xml":"https://content.openalex.org/works/W2999007559.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1530744624","https://openalex.org/W1547479063","https://openalex.org/W1551519020","https://openalex.org/W2017899631","https://openalex.org/W2021480278","https://openalex.org/W2050039992","https://openalex.org/W2171905396","https://openalex.org/W2343849816","https://openalex.org/W2730912875","https://openalex.org/W2752853835","https://openalex.org/W2752908210","https://openalex.org/W4212838771"],"related_works":["https://openalex.org/W3194471551","https://openalex.org/W4375956809","https://openalex.org/W1581373162","https://openalex.org/W2784911598","https://openalex.org/W4297950433","https://openalex.org/W4287023968","https://openalex.org/W4288279572","https://openalex.org/W4247734921","https://openalex.org/W4287905741","https://openalex.org/W4280528977"],"abstract_inverted_index":{"Consider,":[0],"for":[1,30,42,61,138],"a":[2,20,35,88],"permutation":[3],"$\\sigma":[4,99],"\\in":[5,100],"{\\cal":[6,101],"S}_k$,":[7],"the":[8,49,57,64,79,83,122,136],"number":[9],"$F(n,\\sigma)$":[10],"of":[11,24,66,82],"permutations":[12],"in":[13],"${\\cal":[14],"S}_n$":[15],"which":[16],"avoid":[17],"$\\sigma$":[18,32],"as":[19,103],"subpattern.":[21],"The":[22],"conjecture":[23,84,115,130],"Stanley":[25],"and":[26,69,125],"Wilf":[27],"is":[28,34,70,121,135],"that":[29,41,60,78,107,116,131],"every":[31,62],"there":[33],"constant":[36],"$c(\\sigma)":[37],"<":[38],"\\infty$":[39],"such":[40],"all":[43,98],"$n$,":[44],"$F(n,\\sigma)":[45],"\\leq":[46],"c(\\sigma)^n$.":[47],"All":[48],"recent":[50],"work":[51],"on":[52],"this":[53,73,108],"problem":[54],"also":[55,94],"mentions":[56],"\"stronger":[58],"conjecture\"":[59],"$\\sigma$,":[63],"limit":[65],"$F(n,\\sigma)^{1/n}$":[67],"exists":[68],"finite.":[71],"In":[72],"short":[74],"note":[75],"we":[76,114,126],"prove":[77,106],"two":[80],"versions":[81],"are":[85],"equivalent,":[86],"with":[87,112],"simple":[89],"argument":[90],"involving":[91],"subadditivity":[92],"We":[93,105],"discuss":[95],"$n$-permutations,":[96],"containing":[97],"S}_k$":[102],"subpatterns.":[104],"can":[109],"be":[110],"achieved":[111],"$n=k^2$,":[113],"asymptotically":[117],"$n":[118,132],"\\sim":[119,133],"(k/e)^2$":[120],"best":[123],"achievable,":[124],"present":[127],"Noga":[128],"Alon's":[129],"(k/2)^2$":[134],"threshold":[137],"random":[139],"permutations.":[140]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}