{"id":"https://openalex.org/W2131227897","doi":"https://doi.org/10.1017/s0963548308009607","title":"On the Likely Number of Solutions for the Stable Marriage Problem","display_name":"On the Likely Number of Solutions for the Stable Marriage Problem","publication_year":2008,"publication_date":"2008-12-04","ids":{"openalex":"https://openalex.org/W2131227897","doi":"https://doi.org/10.1017/s0963548308009607","mag":"2131227897"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548308009607","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548308009607","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","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/A5078232467","display_name":"Craig Lennon","orcid":null},"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":"CRAIG LENNON","raw_affiliation_strings":["Department of Mathematics, The Ohio State University, 231 W. 18th Ave., Columbus, OH 43210, USA (e-mail:","Department of mathematics, the ohio state university, 231 w. 18th ave., columbus, oh 43210, usa (e-mail: lennon@math.ohio-state.edu, bgp@math.ohio-state.edu)#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Ohio State University, 231 W. 18th Ave., Columbus, OH 43210, USA (e-mail:","institution_ids":["https://openalex.org/I52357470"]},{"raw_affiliation_string":"Department of mathematics, the ohio state university, 231 w. 18th ave., columbus, oh 43210, usa (e-mail: lennon@math.ohio-state.edu, bgp@math.ohio-state.edu)#TAB#","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"last","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":false,"raw_author_name":"BORIS PITTEL","raw_affiliation_strings":["Department of Mathematics, The Ohio State University, 231 W. 18th Ave., Columbus, OH 43210, USA (e-mail:","Department of mathematics, the ohio state university, 231 w. 18th ave., columbus, oh 43210, usa (e-mail: lennon@math.ohio-state.edu, bgp@math.ohio-state.edu)#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Ohio State University, 231 W. 18th Ave., Columbus, OH 43210, USA (e-mail:","institution_ids":["https://openalex.org/I52357470"]},{"raw_affiliation_string":"Department of mathematics, the ohio state university, 231 w. 18th ave., columbus, oh 43210, usa (e-mail: lennon@math.ohio-state.edu, bgp@math.ohio-state.edu)#TAB#","institution_ids":["https://openalex.org/I52357470"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5078232467"],"corresponding_institution_ids":["https://openalex.org/I52357470"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.17818897,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"18","issue":"3","first_page":"371","last_page":"421"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9725000262260437,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9262999892234802,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stable-marriage-problem","display_name":"Stable marriage problem","score":0.8292388319969177},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7489633560180664},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.7060548663139343},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6949200630187988},{"id":"https://openalex.org/keywords/preference","display_name":"Preference","score":0.6683644652366638},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6011383533477783},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.5961422920227051},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.59157395362854},{"id":"https://openalex.org/keywords/fraction","display_name":"Fraction (chemistry)","score":0.5714929103851318},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5130888223648071},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4650935232639313},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.437799334526062},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4221540093421936},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2644622325897217},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1213342547416687},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.059780627489089966},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.05394884943962097}],"concepts":[{"id":"https://openalex.org/C146393371","wikidata":"https://www.wikidata.org/wiki/Q620702","display_name":"Stable marriage problem","level":3,"score":0.8292388319969177},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7489633560180664},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.7060548663139343},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6949200630187988},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.6683644652366638},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6011383533477783},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.5961422920227051},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.59157395362854},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.5714929103851318},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5130888223648071},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4650935232639313},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.437799334526062},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4221540093421936},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2644622325897217},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1213342547416687},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.059780627489089966},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.05394884943962097},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0963548308009607","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548308009607","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/5","display_name":"Gender equality","score":0.7200000286102295}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W568087019","https://openalex.org/W1981139087","https://openalex.org/W1985690205","https://openalex.org/W1990302986","https://openalex.org/W1991220215","https://openalex.org/W2017008045","https://openalex.org/W2056099894","https://openalex.org/W2060445186","https://openalex.org/W2068115726","https://openalex.org/W2086852721","https://openalex.org/W2091887239","https://openalex.org/W2115159265","https://openalex.org/W2169071224","https://openalex.org/W2576544140","https://openalex.org/W2751862591","https://openalex.org/W2946234461","https://openalex.org/W3037173771","https://openalex.org/W3098030202","https://openalex.org/W4235234911","https://openalex.org/W4299432846","https://openalex.org/W6654305506","https://openalex.org/W6785389392"],"related_works":["https://openalex.org/W2931602588","https://openalex.org/W4281738643","https://openalex.org/W4322508012","https://openalex.org/W3123407378","https://openalex.org/W2072430061","https://openalex.org/W2054731762","https://openalex.org/W4224297439","https://openalex.org/W4249871498","https://openalex.org/W4224258059","https://openalex.org/W4236298560"],"abstract_inverted_index":{"An":[0],"instance":[1,64,92],"of":[2,20,25,37,65,114,118,129,143,150,161,170],"a":[3,28,35,90],"size-":[4],"n":[5,10,13,38,99,102,120,122,131,153,155,177],"stable":[6,42,74,84,115],"marriage":[7,30,66],"problem":[8,171],"involves":[9],"men":[11],"and":[12,47,76],"women,":[14],"each":[15,50],"individually":[16],"ranking":[17],"all":[18,97],"members":[19],"opposite":[21],"sex":[22],"in":[23,55],"order":[24,119,130,151],"preference":[26],"as":[27],"potential":[29],"partner.":[31],"A":[32],"complete":[33],"matching,":[34,75],"set":[36],"marriages,":[39],"is":[40,59,88,117,128,146,179,186],"called":[41],"if":[43],"no":[44],"unmatched":[45],"man":[46],"woman":[48],"prefer":[49],"other":[51],"to":[52,148,188],"their":[53],"partners":[54],"the":[56,111,140,162,168],"matching.":[57],"It":[58],"known":[60],"that,":[61],"for":[62],"every":[63],"partner":[67],"preferences,":[68],"there":[69,78],"exists":[70],"at":[71,135,180],"least":[72,181],"one":[73],"that":[77,110,144,167],"are":[79],"instances":[80,172],"with":[81,173],"exponentially":[82],"many":[83],"matchings.":[85],"Our":[86],"focus":[87],"on":[89],"random":[91],"chosen":[93],"uniformly":[94],"from":[95],"among":[96],"(":[98,152],"!)":[100],"2":[101,157],"possible":[103],"instances.":[104],"The":[105,159],"second":[106,141],"author":[107],"had":[108],"proved":[109],"expected":[112],"number":[113,145],"marriages":[116],"ln":[121,154,176],",":[123],"while":[124],"its":[125],"likely":[126],"value":[127],"1/2\u2212":[132],"o":[133],"(1)":[134],"least.":[136],"In":[137],"this":[138,184],"paper":[139],"moment":[142,164],"shown":[147],"be":[149],")":[156],".":[158],"combination":[160],"two":[163],"estimates":[165],"implies":[166],"fraction":[169,185],"roughly":[174],"cn":[175],"solutions":[178],"0.84.":[182],"Whether":[183],"asymptotic":[187],"1":[189],"remains":[190],"an":[191],"open":[192],"question.":[193]},"counts_by_year":[{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2}],"updated_date":"2026-01-15T23:16:33.117629","created_date":"2025-10-10T00:00:00"}