{"id":"https://openalex.org/W2003602731","doi":"https://doi.org/10.1017/s0963548311000459","title":"Counting Certain Pairings in Arbitrary Groups","display_name":"Counting Certain Pairings in Arbitrary Groups","publication_year":2011,"publication_date":"2011-10-11","ids":{"openalex":"https://openalex.org/W2003602731","doi":"https://doi.org/10.1017/s0963548311000459","mag":"2003602731"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548311000459","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548311000459","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/A5108518802","display_name":"Yahya Ould Hamidoune","orcid":null},"institutions":[{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Y. O. HAMIDOUNE","raw_affiliation_strings":["Universit\u00e9 Pierre et Marie Curie (Paris 6), Institut de Math\u00e9matiques de Jussieu, Combinatoire et Optimisation, Case 189, 4 Place Jussieu, 75005 Paris, France","Universit\u00e9 pierre et marie curie (paris 6), institut de math\u00e9matiques de jussieu, combinatoire et optimisation, case 189, 4 place jussieu, 75005 paris, france#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Pierre et Marie Curie (Paris 6), Institut de Math\u00e9matiques de Jussieu, Combinatoire et Optimisation, Case 189, 4 Place Jussieu, 75005 Paris, France","institution_ids":["https://openalex.org/I3017942884","https://openalex.org/I39804081"]},{"raw_affiliation_string":"Universit\u00e9 pierre et marie curie (paris 6), institut de math\u00e9matiques de jussieu, combinatoire et optimisation, case 189, 4 place jussieu, 75005 paris, france#TAB#","institution_ids":["https://openalex.org/I3017942884"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5108518802"],"corresponding_institution_ids":["https://openalex.org/I3017942884","https://openalex.org/I39804081"],"apc_list":null,"apc_paid":null,"fwci":0.4206,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.5403705,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"20","issue":"6","first_page":"855","last_page":"865"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9983000159263611,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9983000159263611,"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/T11797","display_name":"graph theory and CDMA systems","score":0.996399998664856,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9944999814033508,"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/bijection","display_name":"Bijection","score":0.6955137848854065},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6822614073753357},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6656879782676697},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.6284465789794922},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5864920616149902},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4868246912956238},{"id":"https://openalex.org/keywords/pairing","display_name":"Pairing","score":0.4306091070175171},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4232883155345917},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.4124421179294586},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12884730100631714},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10993263125419617}],"concepts":[{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.6955137848854065},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6822614073753357},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6656879782676697},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.6284465789794922},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5864920616149902},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4868246912956238},{"id":"https://openalex.org/C14103023","wikidata":"https://www.wikidata.org/wiki/Q11681459","display_name":"Pairing","level":3,"score":0.4306091070175171},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4232883155345917},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.4124421179294586},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12884730100631714},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10993263125419617},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C54101563","wikidata":"https://www.wikidata.org/wiki/Q124131","display_name":"Superconductivity","level":2,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","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},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0963548311000459","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548311000459","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W107838738","https://openalex.org/W842301775","https://openalex.org/W1498486822","https://openalex.org/W1569269406","https://openalex.org/W1979447587","https://openalex.org/W2001510560","https://openalex.org/W2010386855","https://openalex.org/W2013185619","https://openalex.org/W2014421955","https://openalex.org/W2024564433","https://openalex.org/W2028369791","https://openalex.org/W2034012450","https://openalex.org/W2054902784","https://openalex.org/W2063292248","https://openalex.org/W2067592849","https://openalex.org/W2068854759","https://openalex.org/W2157024420","https://openalex.org/W2315173711","https://openalex.org/W2984164607","https://openalex.org/W3009548514","https://openalex.org/W6604438047","https://openalex.org/W6653874152"],"related_works":["https://openalex.org/W2030171229","https://openalex.org/W2583084574","https://openalex.org/W4302428509","https://openalex.org/W1974527570","https://openalex.org/W2950604330","https://openalex.org/W2017807608","https://openalex.org/W2039857505","https://openalex.org/W2972447449","https://openalex.org/W3007692637","https://openalex.org/W132200507"],"abstract_inverted_index":{"In":[0,174],"this":[1,122],"paper,":[2],"we":[3,118,134],"study":[4],"certain":[5],"pairings":[6,57],"which":[7,161],"are":[8,16],"defined":[9],"as":[10],"follows:":[11],"if":[12],"A":[13,29,37,45,63,71,74,91,126,143,165,177],"and":[14,75,97,151,166],"B":[15,27,35,51,76,88,95,107,111,149,159,167,179,185],"finite":[17,79],"subsets":[18,80],"of":[19,55,81,103,106,147,154,189],"an":[20,82,136],"arbitrary":[21,83],"group,":[22],"a":[23,31,169,187,190],"Wakeford\u2013Fan\u2013Losonczy":[24],"pairing":[25],"from":[26],"onto":[28],"is":[30,58,108,128,162,186],"bijection":[32],"\u03c6":[33],":":[34],"\u2192":[36],"such":[38,56],"that":[39,100,120],"b":[40,42,49],"\u03c6(":[41],")":[43,72,127,144],"\u2209":[44,87],",":[46,77,89,160,180],"for":[47,73],"every":[48,104],"\u2208":[50],".":[52],"The":[53],"number":[54],"denoted":[59],"by":[60,158],"\u03bc(":[61,69,124,141],"B,":[62,70,125,142],").":[64],"We":[65],"investigate":[66],"the":[67,98,101,152,155,175],"quantity":[68],"two":[78],"group":[84,156],"satisfying":[85],"1":[86],"|":[90,92,94,110,112,148,150],"=":[93,178],"|,":[96],"fact":[99],"order":[102],"element":[105],"\u2265":[109],"+":[113],"1.":[114],"Extending":[115],"earlier":[116],"results,":[117],"show":[119],"in":[121,145],"case,":[123],"never":[129],"equal":[130],"to":[131],"0.":[132],"Furthermore":[133],"prove":[135],"explicit":[137],"lower":[138],"bound":[139,182],"on":[140],"terms":[146],"cardinality":[153],"generated":[157],"valid":[163],"unless":[164,184],"have":[168],"special":[170],"form":[171],"explicitly":[172],"described.":[173],"case":[176],"our":[181],"holds":[183],"translate":[188],"progression.":[191]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
