{"id":"https://openalex.org/W2471383395","doi":"https://doi.org/10.37236/6225","title":"Large Deviations for Permutations Avoiding Monotone Patterns","display_name":"Large Deviations for Permutations Avoiding Monotone Patterns","publication_year":2016,"publication_date":"2016-12-09","ids":{"openalex":"https://openalex.org/W2471383395","doi":"https://doi.org/10.37236/6225","mag":"2471383395"},"language":"en","primary_location":{"id":"doi:10.37236/6225","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6225","pdf_url":null,"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":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37236/6225","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089177276","display_name":"Neal Madras","orcid":"https://orcid.org/0000-0003-2981-3577"},"institutions":[{"id":"https://openalex.org/I192455969","display_name":"York University","ror":"https://ror.org/05fq50484","country_code":"CA","type":"education","lineage":["https://openalex.org/I192455969"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Neal Madras","raw_affiliation_strings":["York University"],"affiliations":[{"raw_affiliation_string":"York University","institution_ids":["https://openalex.org/I192455969"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026976460","display_name":"Lerna Pehlivan","orcid":"https://orcid.org/0000-0002-4940-5813"},"institutions":[{"id":"https://openalex.org/I163902620","display_name":"Mount Allison University","ror":"https://ror.org/03grc6f14","country_code":"CA","type":"education","lineage":["https://openalex.org/I163902620"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Lerna Pehlivan","raw_affiliation_strings":["Mount Allison University","Mount Allison University,"],"affiliations":[{"raw_affiliation_string":"Mount Allison University","institution_ids":["https://openalex.org/I163902620"]},{"raw_affiliation_string":"Mount Allison University,","institution_ids":["https://openalex.org/I163902620"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089177276"],"corresponding_institution_ids":["https://openalex.org/I192455969"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.039503,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"23","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11716","display_name":"Random Matrices and Applications","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7428123354911804},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.6135104298591614},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.6050492525100708},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.5421867966651917},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.5286427140235901},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.5234382152557373},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5062938928604126},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.48514947295188904},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3962125778198242},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1406523585319519},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.12595564126968384},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12315782904624939}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7428123354911804},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6135104298591614},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.6050492525100708},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.5421867966651917},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.5286427140235901},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.5234382152557373},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5062938928604126},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.48514947295188904},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3962125778198242},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1406523585319519},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12595564126968384},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12315782904624939},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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":4,"locations":[{"id":"doi:10.37236/6225","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6225","pdf_url":null,"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:1606.07906","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1606.07906","pdf_url":"https://arxiv.org/pdf/1606.07906","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"},{"id":"mag:2471383395","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1606.07906.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1606.07906","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1606.07906","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.37236/6225","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6225","pdf_url":null,"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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1984841421","https://openalex.org/W2015106956","https://openalex.org/W2050039992","https://openalex.org/W2057808121","https://openalex.org/W2091015960","https://openalex.org/W2400363291","https://openalex.org/W2751862591","https://openalex.org/W2752853835","https://openalex.org/W2885507564","https://openalex.org/W2951079287","https://openalex.org/W2951899095","https://openalex.org/W2963605795","https://openalex.org/W2999007559"],"related_works":["https://openalex.org/W2963384515","https://openalex.org/W2116841368","https://openalex.org/W2980348586","https://openalex.org/W2337974484","https://openalex.org/W1965481559","https://openalex.org/W2298662281","https://openalex.org/W2952757072","https://openalex.org/W1529455780","https://openalex.org/W3160382400","https://openalex.org/W1998234397","https://openalex.org/W2972367164","https://openalex.org/W2950341024","https://openalex.org/W2887748158","https://openalex.org/W3102586875","https://openalex.org/W2964112947","https://openalex.org/W2026906087","https://openalex.org/W1997308494","https://openalex.org/W2267640490","https://openalex.org/W2085271862","https://openalex.org/W3110735507"],"abstract_inverted_index":{"For":[0,24],"a":[1],"given":[2],"permutation":[3],"$\\tau$,":[4],"let":[5],"$P_N^{\\tau}$":[6],"be":[7],"the":[8,13,21,52,57,64,82,87],"uniform":[9],"probability":[10,58],"distribution":[11],"on":[12],"set":[14],"of":[15,67,84],"$N$-element":[16],"permutations":[17],"$\\sigma$":[18],"that":[19,72],"avoid":[20],"pattern":[22],"$\\tau$.":[23],"$\\tau=\\mu_k:=123\\ldots":[25],"k$,":[26],"we":[27,49,62],"consider":[28],"$P_N^{\\mu_k}(\\sigma_I=J)$":[29],"where":[30],"$I\\sim":[31],"\\gamma":[32],"N$":[33,37],"and":[34,61,80],"$J\\sim":[35],"\\delta":[36,40,45],"for":[38,73,90],"$\\gamma,":[39],"\\in":[41],"(0,1)$.":[42],"If":[43],"$\\gamma+":[44],"\\neq":[46],"1$,":[47],"then":[48],"are":[50],"in":[51],"large":[53],"deviations":[54],"regime":[55],"with":[56],"decaying":[59],"exponentially,":[60],"calculate":[63],"limiting":[65],"value":[66],"$P_N^{\\mu_k}(\\sigma_I=J)^{1/N}$.":[68],"We":[69],"also":[70],"observe":[71],"$\\tau":[74],"=":[75],"\\lambda_{k,\\ell}":[76],":=":[77],"12\\ldots\\ell":[78],"k(k-1)\\ldots(\\ell+1)$":[79],"$\\gamma+\\delta&lt;1$,":[81],"limit":[83],"$P_N^{\\tau}(\\sigma_I=J)^{1/N}$":[85],"is":[86],"same":[88],"as":[89],"$\\tau=\\mu_k$.":[91]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
