{"id":"https://openalex.org/W1990949698","doi":"https://doi.org/10.1137/1033051","title":"A Generalized Birthday Problem","display_name":"A Generalized Birthday Problem","publication_year":1991,"publication_date":"1991-06-01","ids":{"openalex":"https://openalex.org/W1990949698","doi":"https://doi.org/10.1137/1033051","mag":"1990949698"},"language":"en","primary_location":{"id":"doi:10.1137/1033051","is_oa":false,"landing_page_url":"https://doi.org/10.1137/1033051","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","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/A5109950116","display_name":"Frank H. Mathis","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Frank H. Mathis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5109950116"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8237,"has_fulltext":false,"cited_by_count":61,"citation_normalized_percentile":{"value":0.58958838,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"33","issue":"2","first_page":"265","last_page":"270"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9926000237464905,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9926000237464905,"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"}},{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9926000237464905,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9921000003814697,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7262498736381531},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5597168803215027},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5588191747665405},{"id":"https://openalex.org/keywords/sample-size-determination","display_name":"Sample size determination","score":0.5002527236938477},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.4907773435115814},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.4815981090068817},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4184427857398987},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3255004286766052},{"id":"https://openalex.org/keywords/demography","display_name":"Demography","score":0.11098867654800415},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08209553360939026}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7262498736381531},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5597168803215027},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5588191747665405},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.5002527236938477},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.4907773435115814},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.4815981090068817},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4184427857398987},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3255004286766052},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.11098867654800415},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08209553360939026},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/1033051","is_oa":false,"landing_page_url":"https://doi.org/10.1137/1033051","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.5}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4388813866","https://openalex.org/W2999104021","https://openalex.org/W4293088233","https://openalex.org/W2850804095","https://openalex.org/W1481656249","https://openalex.org/W2162280767","https://openalex.org/W1570799877","https://openalex.org/W2800688113","https://openalex.org/W4236933217","https://openalex.org/W2057598446"],"abstract_inverted_index":{"A":[0],"generalized":[1],"version":[2],"of":[3,13,32,50,60,85,94],"the":[4,47,54,61,64,95],"birthday":[5],"problem":[6],"is":[7,35,46,67,89,97],"as":[8,82],"follows.":[9],"Suppose":[10],"each":[11],"member":[12],"a":[14,18,29,83],"population":[15],"independently":[16],"receives":[17],"number":[19,66],"randomly":[20],"selected":[21],"from":[22],"$\\{":[23],"{1,2,3,":[24],"\\cdots":[25],",x}":[26],"\\}$,":[27],"and":[28,74],"random":[30],"sample":[31,62],"size":[33],"n":[34,51,81],"to":[36,79],"be":[37],"taken.":[38],"If":[39],"$0":[40],"<":[41,43],"p":[42,88],"1$,":[44],"what":[45],"smallest":[48],"value":[49],"so":[52],"that":[53,56],"probability":[55],"at":[57,68],"least":[58,69],"two":[59],"have":[63],"same":[65],"p?":[70],"Both":[71],"empirical":[72],"modeling":[73],"approximation":[75,96],"techniques":[76],"are":[77],"used":[78],"determine":[80],"function":[84],"x":[86],"when":[87],"fixed.":[90],"An":[91],"error":[92],"analysis":[93],"presented.":[98]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
