{"id":"https://openalex.org/W2050968221","doi":"https://doi.org/10.1002/(sici)1098-2418(199903)14:2<185::aid-rsa4>3.0.co;2-f","title":"On the multiplicity of parts in a random partition","display_name":"On the multiplicity of parts in a random partition","publication_year":1999,"publication_date":"1999-03-01","ids":{"openalex":"https://openalex.org/W2050968221","doi":"https://doi.org/10.1002/(sici)1098-2418(199903)14:2<185::aid-rsa4>3.0.co;2-f","mag":"2050968221"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1098-2418(199903)14:2<185::aid-rsa4>3.0.co;2-f","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1098-2418(199903)14:2<185::aid-rsa4>3.0.co;2-f","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Random Structures and Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038635373","display_name":"Sylvie Corteel","orcid":"https://orcid.org/0000-0003-4669-4653"},"institutions":[{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]},{"id":"https://openalex.org/I4210144804","display_name":"Laboratoire de Recherche en Informatique","ror":"https://ror.org/04e3ktk27","country_code":"FR","type":"facility","lineage":["https://openalex.org/I102197404","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210144804","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Sylvie Corteel","raw_affiliation_strings":["Laboratoire de Recherche en Informatique, Universite\u0301 Paris-Sud, 91405 Orsay, France","Supported in part by NSF grant DMS9302505","Laboratoire de Recherche en Informatique, Universit\u00e9 Paris-Sud, 91405 Orsay, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire de Recherche en Informatique, Universite\u0301 Paris-Sud, 91405 Orsay, France","institution_ids":["https://openalex.org/I4210144804","https://openalex.org/I102197404"]},{"raw_affiliation_string":"Supported in part by NSF grant DMS9302505","institution_ids":[]},{"raw_affiliation_string":"Laboratoire de Recherche en Informatique, Universit\u00e9 Paris-Sud, 91405 Orsay, France","institution_ids":["https://openalex.org/I4210144804","https://openalex.org/I102197404"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084113050","display_name":"Boris Pittel","orcid":"https://orcid.org/0000-0003-1875-9317"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Boris Pittel","raw_affiliation_strings":["Department of Mathematics, Ohio State University, Columbus, OH 43210","Supported by the Focus on Discrete Probability Program at the Dimacs Center of Rutgers University, and by NSA grant MDA-904-96-1-0053"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ohio State University, Columbus, OH 43210","institution_ids":["https://openalex.org/I52357470"]},{"raw_affiliation_string":"Supported by the Focus on Discrete Probability Program at the Dimacs Center of Rutgers University, and by NSA grant MDA-904-96-1-0053","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029085327","display_name":"Carla D. Savage","orcid":null},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Carla D. Savage","raw_affiliation_strings":["Department of Computer Science, North Carolina State University, Raleigh, NC 27695-8206","Supported in part by NSF grant DMS96227722"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, North Carolina State University, Raleigh, NC 27695-8206","institution_ids":["https://openalex.org/I137902535"]},{"raw_affiliation_string":"Supported in part by NSF grant DMS96227722","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112203336","display_name":"Herbert S. Wilf","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":"Herbert S. Wilf","raw_affiliation_strings":["Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104-6395"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104-6395","institution_ids":["https://openalex.org/I79576946"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5029085327","https://openalex.org/A5038635373","https://openalex.org/A5084113050","https://openalex.org/A5112203336"],"corresponding_institution_ids":["https://openalex.org/I102197404","https://openalex.org/I137902535","https://openalex.org/I4210144804","https://openalex.org/I52357470","https://openalex.org/I79576946"],"apc_list":{"value":4330,"currency":"USD","value_usd":4330},"apc_paid":null,"fwci":5.0866,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.95776631,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"14","issue":"2","first_page":"185","last_page":"197"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9987000226974487,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9977999925613403,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9919000267982483,"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/mathematics","display_name":"Mathematics","score":0.7771528959274292},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.7368701696395874},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6912857294082642},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6661551594734192},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.477488249540329},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.4523514211177826},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10064873099327087},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06384041905403137}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7771528959274292},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.7368701696395874},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6912857294082642},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6661551594734192},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.477488249540329},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4523514211177826},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10064873099327087},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06384041905403137}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1098-2418(199903)14:2<185::aid-rsa4>3.0.co;2-f","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1098-2418(199903)14:2<185::aid-rsa4>3.0.co;2-f","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Random Structures and Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1198302060","https://openalex.org/W1550603695","https://openalex.org/W1969902736","https://openalex.org/W1996847651","https://openalex.org/W1999312242","https://openalex.org/W2013832448","https://openalex.org/W2024384464","https://openalex.org/W2058488357","https://openalex.org/W2063302961","https://openalex.org/W2065294359","https://openalex.org/W2083411831","https://openalex.org/W3031984517","https://openalex.org/W4212799367","https://openalex.org/W4213095169","https://openalex.org/W4299811363"],"related_works":["https://openalex.org/W2808944898","https://openalex.org/W3196207352","https://openalex.org/W2951724202","https://openalex.org/W3084261076","https://openalex.org/W1996614773","https://openalex.org/W4387820098","https://openalex.org/W2576399385","https://openalex.org/W2963408011","https://openalex.org/W4236324517","https://openalex.org/W1586813864"],"abstract_inverted_index":{"Let":[0,17],"\u03bb":[1,53],"be":[2,19],"a":[3,20,65,70,121,127,147],"partition":[4,72,129],"of":[5,30,84,102,106,108,120,126,130,139,144,150],"an":[6,90,99],"integer":[7],"n":[8,131],"chosen":[9,23,123],"uniformly":[10,24],"at":[11,25],"random":[12,26,66,71,128],"among":[13],"all":[14,31],"such":[15],"partitions.":[16],"s(\u03bb)":[18,48],"part":[21,32,67,86,124],"size":[22,68,125],"from":[27],"the":[28,45,61,81,103,117,140],"set":[29],"sizes":[33],"that":[34,47,64,116],"occur":[35],"in":[36,52,69],"\u03bb.":[37],"We":[38],"prove":[39],"that,":[40],"for":[41,59,80],"every":[42],"fixed":[43],"m\u22651,":[44],"probability":[46,63],"has":[49],"multiplicity":[50,110,119],"m":[51],"approaches":[54],"1/(m(m+1))":[55],"as":[56],"n\u2192\u221e.":[57],"Thus,":[58],"example,":[60],"limiting":[62],"is":[73,75,132],"unrepeated":[74],"1/2.":[76],"In":[77],"addition,":[78],"(a)":[79],"average":[82,104],"number":[83,105],"different":[85],"sizes,":[87],"we":[88,97,114],"refine":[89],"asymptotic":[91,100,133],"estimate":[92,101],"given":[93,109],"by":[94],"Wilf,":[95],"(b)":[96],"derive":[98],"parts":[107],"m,":[111],"and":[112,143],"(c)":[113,145],"show":[115],"expected":[118],"randomly":[122],"to":[134],"(log":[135],"n)/2.":[136],"The":[137],"proofs":[138],"main":[141],"result":[142],"use":[146],"conditioning":[148],"device":[149],"Fristedt.":[151],"\u00a91999":[152],"John":[153],"Wiley":[154],"&":[155],"Sons,":[156],"Inc.":[157],"Random":[158],"Struct.":[159],"Alg.,":[160],"14,":[161],"185\u2013197,":[162],"1999":[163]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
