{"id":"https://openalex.org/W1494260032","doi":"https://doi.org/10.37236/188","title":"Profiles of Permutations","display_name":"Profiles of Permutations","publication_year":2009,"publication_date":"2009-08-07","ids":{"openalex":"https://openalex.org/W1494260032","doi":"https://doi.org/10.37236/188","mag":"1494260032"},"language":"en","primary_location":{"id":"doi:10.37236/188","is_oa":true,"landing_page_url":"https://doi.org/10.37236/188","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r99/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/v16i1r99/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049063468","display_name":"Michael Lugo","orcid":null},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michael Lugo","raw_affiliation_strings":["Department of Mathematics University of Pennsylvania Philadelphia, PA 19104","#N#               * University of Pennsylvania"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Pennsylvania Philadelphia, PA 19104","institution_ids":["https://openalex.org/I79576946"]},{"raw_affiliation_string":"#N#               * University of Pennsylvania","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5049063468"],"corresponding_institution_ids":["https://openalex.org/I79576946"],"apc_list":null,"apc_paid":null,"fwci":3.1614,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.91728678,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"16","issue":"1","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":0.9998000264167786,"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":0.9998000264167786,"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":0.984000027179718,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9829999804496765,"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/mathematics","display_name":"Mathematics","score":0.8429708480834961},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7453572750091553},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.6474081873893738},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.6339112520217896},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.5533784627914429},{"id":"https://openalex.org/keywords/random-permutation","display_name":"Random permutation","score":0.47552087903022766},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4620349705219269},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4468734860420227},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4210375249385834},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3694472908973694},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.19444099068641663},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14423060417175293},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10126858949661255}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8429708480834961},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7453572750091553},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6474081873893738},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.6339112520217896},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5533784627914429},{"id":"https://openalex.org/C200985842","wikidata":"https://www.wikidata.org/wiki/Q3375503","display_name":"Random permutation","level":3,"score":0.47552087903022766},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4620349705219269},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4468734860420227},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4210375249385834},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3694472908973694},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.19444099068641663},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14423060417175293},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10126858949661255},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"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},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/188","is_oa":true,"landing_page_url":"https://doi.org/10.37236/188","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r99/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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.214.3626","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.3626","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_16/PDF/v16i1r99.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.314.3934","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.314.3934","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0907.5351v1.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/188","is_oa":true,"landing_page_url":"https://doi.org/10.37236/188","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r99/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":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.6499999761581421}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1494260032.pdf","grobid_xml":"https://content.openalex.org/works/W1494260032.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W186403072","https://openalex.org/W1489554514","https://openalex.org/W1491916424","https://openalex.org/W1540048281","https://openalex.org/W1541405245","https://openalex.org/W1544198293","https://openalex.org/W1551893515","https://openalex.org/W1597723816","https://openalex.org/W1622968791","https://openalex.org/W1967318355","https://openalex.org/W1967677618","https://openalex.org/W1982202832","https://openalex.org/W2018919817","https://openalex.org/W2019881480","https://openalex.org/W2045390532","https://openalex.org/W2074879947","https://openalex.org/W2078453580","https://openalex.org/W2084902365","https://openalex.org/W2085901659","https://openalex.org/W2092866774","https://openalex.org/W2103268360","https://openalex.org/W2110522712","https://openalex.org/W2119740160","https://openalex.org/W2126891388","https://openalex.org/W2142554063","https://openalex.org/W2169071224","https://openalex.org/W2226303357","https://openalex.org/W2276336683","https://openalex.org/W2340541605","https://openalex.org/W2500470525","https://openalex.org/W2576544140","https://openalex.org/W4231616774","https://openalex.org/W4241642706"],"related_works":["https://openalex.org/W4318195686","https://openalex.org/W2975999359","https://openalex.org/W4287173569","https://openalex.org/W2796561647","https://openalex.org/W4280497496","https://openalex.org/W4313513739","https://openalex.org/W3119693376","https://openalex.org/W3182422617","https://openalex.org/W2244208494","https://openalex.org/W4313557239"],"abstract_inverted_index":{"This":[0],"paper":[1],"develops":[2],"an":[3,23],"analogy":[4],"between":[5,149],"the":[6,11,33,40,51,73,89,93,106,112,150,154],"cycle":[7,17,121],"structure":[8],"of,":[9],"on":[10,32],"one":[12],"hand,":[13,35],"random":[14,58,116],"permutations":[15,36,59,101,137,165],"with":[16,27,43,62,66,76,109,138,143],"lengths":[18],"restricted":[19],"to":[20,39],"lie":[21],"in":[22,100,119],"infinite":[24],"set":[25],"$S$":[26],"asymptotic":[28,52],"density":[29],"$\\sigma$":[30],"and,":[31],"other":[34],"selected":[37],"according":[38],"Ewens":[41,74,107,151],"distribution":[42,75,108,152],"parameter":[44,77,110],"$\\sigma$.":[45,145],"In":[46],"particular":[47],"we":[48,97],"show":[49,98],"that":[50,99],"expected":[53],"number":[54],"of":[55,57,60,92,102,114],"cycles":[56,64,68,139],"$[n]$":[61,103],"all":[63,67,80],"even,":[65],"odd,":[69],"and":[70,88,153,157],"chosen":[71,104],"from":[72,105,167],"$1/2$":[78],"are":[79],"${1":[81],"\\over":[82],"2}":[83],"\\log":[84],"n":[85],"+":[86],"O(1)$,":[87],"variance":[90],"is":[91],"same":[94,132],"order.":[95],"Furthermore,":[96],"$\\sigma$,":[111],"probability":[113],"a":[115,120],"element":[117],"being":[118],"longer":[122],"than":[123],"$\\gamma":[124],"n$":[125],"approaches":[126],"$(1-\\gamma)^\\sigma$":[127],"for":[128,136],"large":[129],"$n$.":[130],"The":[131],"limit":[133],"law":[134],"holds":[135],"carrying":[140],"multiplicative":[141],"weights":[142],"average":[144],"We":[146],"draw":[147],"parallels":[148,161],"asymptotic-density":[155],"case":[156],"explain":[158],"why":[159],"these":[160],"should":[162],"exist":[163],"using":[164],"drawn":[166],"weighted":[168],"Boltzmann":[169],"distributions.":[170]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}