{"id":"https://openalex.org/W1503443286","doi":"https://doi.org/10.37236/2071","title":"On the Number of Indecomposable Permutations with a Given Number of Cycles","display_name":"On the Number of Indecomposable Permutations with a Given Number of Cycles","publication_year":2012,"publication_date":"2012-02-29","ids":{"openalex":"https://openalex.org/W1503443286","doi":"https://doi.org/10.37236/2071","mag":"1503443286"},"language":"en","primary_location":{"id":"doi:10.37236/2071","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2071","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p49/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/v19i1p49/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040359504","display_name":"Robert Cori","orcid":"https://orcid.org/0000-0001-9776-1196"},"institutions":[{"id":"https://openalex.org/I4210142254","display_name":"Laboratoire Bordelais de Recherche en Informatique","ror":"https://ror.org/03adqg323","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210159245","https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Robert Cori","raw_affiliation_strings":["Laboratoire Bordelais de Recherche en Informatique"],"affiliations":[{"raw_affiliation_string":"Laboratoire Bordelais de Recherche en Informatique","institution_ids":["https://openalex.org/I4210142254"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035864448","display_name":"Claire Mathieu","orcid":"https://orcid.org/0000-0002-0517-112X"},"institutions":[{"id":"https://openalex.org/I4210103330","display_name":"\u00c9cole Normale Sup\u00e9rieure","ror":"https://ror.org/01dp7jr64","country_code":"BI","type":"education","lineage":["https://openalex.org/I4210103330"]}],"countries":["BI"],"is_corresponding":false,"raw_author_name":"Claire Mathieu","raw_affiliation_strings":["D\u00e9partement d'informatique de l'\u00c9cole normale sup\u00e9rieure"],"affiliations":[{"raw_affiliation_string":"D\u00e9partement d'informatique de l'\u00c9cole normale sup\u00e9rieure","institution_ids":["https://openalex.org/I4210103330"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008889141","display_name":"J. M. Robson","orcid":"https://orcid.org/0000-0002-4332-6524"},"institutions":[{"id":"https://openalex.org/I4210142254","display_name":"Laboratoire Bordelais de Recherche en Informatique","ror":"https://ror.org/03adqg323","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210159245","https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"John Michael Robson","raw_affiliation_strings":["Laboratoire Bordelais de Recherche en Informatique"],"affiliations":[{"raw_affiliation_string":"Laboratoire Bordelais de Recherche en Informatique","institution_ids":["https://openalex.org/I4210142254"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5040359504"],"corresponding_institution_ids":["https://openalex.org/I4210142254"],"apc_list":null,"apc_paid":null,"fwci":0.749,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.72758908,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"19","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9977999925613403,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9977999925613403,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9973999857902527,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9958000183105469,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/indecomposable-module","display_name":"Indecomposable module","score":0.8966339230537415},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8820782899856567},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.8394490480422974},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8338533639907837},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.6760992407798767},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6357040405273438},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4741068482398987},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05150464177131653},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.04386153817176819}],"concepts":[{"id":"https://openalex.org/C157480366","wikidata":"https://www.wikidata.org/wiki/Q2499534","display_name":"Indecomposable module","level":2,"score":0.8966339230537415},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8820782899856567},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.8394490480422974},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8338533639907837},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.6760992407798767},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6357040405273438},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4741068482398987},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05150464177131653},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.04386153817176819},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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":1,"locations":[{"id":"doi:10.37236/2071","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2071","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p49/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:10.37236/2071","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2071","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p49/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":[{"id":"https://openalex.org/G3115650792","display_name":null,"funder_award_id":"096403","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3497978841","display_name":"AF:  Medium:  Collaborative Research:  Solutions to Planar Optimization Problems","funder_award_id":"0964037","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1503443286.pdf","grobid_xml":"https://content.openalex.org/works/W1503443286.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W82672431","https://openalex.org/W110387391","https://openalex.org/W186403072","https://openalex.org/W642825766","https://openalex.org/W1489988510","https://openalex.org/W1514324498","https://openalex.org/W1579213680","https://openalex.org/W2001378190","https://openalex.org/W2034398966","https://openalex.org/W2043822055","https://openalex.org/W2097565928","https://openalex.org/W2139572946","https://openalex.org/W2151245892","https://openalex.org/W2325072723","https://openalex.org/W2340541605","https://openalex.org/W2752061190","https://openalex.org/W2752853835","https://openalex.org/W2911361414","https://openalex.org/W2914659449","https://openalex.org/W4300302225"],"related_works":["https://openalex.org/W4237107081","https://openalex.org/W3105245946","https://openalex.org/W2060542026","https://openalex.org/W1630132514","https://openalex.org/W2952207848","https://openalex.org/W4241094354","https://openalex.org/W2090132053","https://openalex.org/W2403307814","https://openalex.org/W4299823074","https://openalex.org/W2152772468"],"abstract_inverted_index":{"A":[0],"permutation":[1,18,28],"$a_1a_2\\ldots":[2,14],"a_n$":[3],"is":[4,16,35,42,67,73],"indecomposable":[5,36],"if":[6],"there":[7,72],"does":[8],"not":[9],"exist":[10],"$p&lt;n$":[11],"such":[12],"that":[13,26,39],"a_p$":[15],"a":[17,27,61,86],"of":[19,29,91],"$\\{":[20],"1,2,\\ldots,p\\}$.":[21],"We":[22],"consider":[23],"the":[24,49,92],"probability":[25,41,51,66],"${\\mathbb":[30],"S}_n$":[31],"with":[32,57],"$m$":[33],"cycles":[34],"and":[37,71],"prove":[38],"this":[40],"monotone":[43,68],"non-increasing":[44],"in":[45,69],"$n$.We":[46],"compute":[47],"also":[48],"asymptotic":[50,65],"when":[52],"$n$":[53],"goes":[54],"to":[55,60,82],"infinity":[56],"$m/n$":[58],"tending":[59],"fixed":[62],"ratio.":[63],"The":[64],"$m/n$,":[70],"no":[74],"threshold":[75],"phenomenon:":[76],"it":[77],"degrades":[78],"gracefully":[79],"from":[80],"1":[81],"0.":[83],"When":[84],"$n=2m$,":[85],"slight":[87],"majority":[88],"($51.117\\ldots$":[89],"percent)":[90],"permutations":[93],"are":[94],"indecomposable.":[95]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
