{"id":"https://openalex.org/W1957229634","doi":"https://doi.org/10.37236/4987","title":"A Deza\u2013Frankl Type Theorem for Set Partitions","display_name":"A Deza\u2013Frankl Type Theorem for Set Partitions","publication_year":2015,"publication_date":"2015-03-30","ids":{"openalex":"https://openalex.org/W1957229634","doi":"https://doi.org/10.37236/4987","mag":"1957229634"},"language":"en","primary_location":{"id":"doi:10.37236/4987","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4987","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p84/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/v22i1p84/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019759019","display_name":"Cheng Yeaw Ku","orcid":"https://orcid.org/0000-0002-8606-3402"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":true,"raw_author_name":"Cheng Yeaw Ku","raw_affiliation_strings":["National University of Singapore"],"affiliations":[{"raw_affiliation_string":"National University of Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069418477","display_name":"Kok Bin Wong","orcid":"https://orcid.org/0000-0001-5640-4432"},"institutions":[{"id":"https://openalex.org/I33849332","display_name":"University of Malaya","ror":"https://ror.org/00rzspn62","country_code":"MY","type":"education","lineage":["https://openalex.org/I33849332"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Kok Bin Wong","raw_affiliation_strings":["University of Malaya"],"affiliations":[{"raw_affiliation_string":"University of Malaya","institution_ids":["https://openalex.org/I33849332"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019759019"],"corresponding_institution_ids":["https://openalex.org/I165932596"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.07496214,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"22","issue":"1","first_page":null,"last_page":null},"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":0.9997000098228455,"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":0.9997000098228455,"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":0.9988999962806702,"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/T10849","display_name":"Finite Group Theory Research","score":0.9970999956130981,"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/combinatorics","display_name":"Combinatorics","score":0.8669395446777344},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6922747492790222},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6837707757949829},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6480749249458313},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5111539959907532},{"id":"https://openalex.org/keywords/singleton","display_name":"Singleton","score":0.4466514587402344}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8669395446777344},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6922747492790222},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6837707757949829},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6480749249458313},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5111539959907532},{"id":"https://openalex.org/C117354338","wikidata":"https://www.wikidata.org/wiki/Q1165112","display_name":"Singleton","level":3,"score":0.4466514587402344},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C2779234561","wikidata":"https://www.wikidata.org/wiki/Q11995","display_name":"Pregnancy","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/4987","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4987","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p84/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:scholarbank.nus.edu.sg:10635/128030","is_oa":false,"landing_page_url":"http://scholarbank.nus.edu.sg/handle/10635/128030","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.37236/4987","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4987","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p84/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/G4108978234","display_name":null,"funder_award_id":"RG367-15AFR","funder_id":"https://openalex.org/F4320322604","funder_display_name":"Universiti Malaya"}],"funders":[{"id":"https://openalex.org/F4320322604","display_name":"Universiti Malaya","ror":"https://ror.org/00rzspn62"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1957229634.pdf"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W1928896618","https://openalex.org/W1969693428","https://openalex.org/W1977358838","https://openalex.org/W1984685721","https://openalex.org/W1987233725","https://openalex.org/W1989716787","https://openalex.org/W1992472342","https://openalex.org/W1992844673","https://openalex.org/W1995238527","https://openalex.org/W1995680324","https://openalex.org/W1998914526","https://openalex.org/W2010775520","https://openalex.org/W2016341899","https://openalex.org/W2019935404","https://openalex.org/W2022917003","https://openalex.org/W2041807026","https://openalex.org/W2047848310","https://openalex.org/W2061880181","https://openalex.org/W2079135110","https://openalex.org/W2083241416","https://openalex.org/W2084490360","https://openalex.org/W2085573719","https://openalex.org/W2093718341","https://openalex.org/W2104078069","https://openalex.org/W2105006061","https://openalex.org/W2121567780","https://openalex.org/W2130523901","https://openalex.org/W2167233799","https://openalex.org/W2168751269","https://openalex.org/W2730836615","https://openalex.org/W2773943437","https://openalex.org/W2949896547","https://openalex.org/W2964279233","https://openalex.org/W3143189643","https://openalex.org/W6606925627","https://openalex.org/W6826309720"],"related_works":["https://openalex.org/W747331120","https://openalex.org/W2351588585","https://openalex.org/W2076370897","https://openalex.org/W4233660055","https://openalex.org/W2906951486","https://openalex.org/W3125437892","https://openalex.org/W2015634066","https://openalex.org/W2069654053","https://openalex.org/W3046629113","https://openalex.org/W2048339306"],"abstract_inverted_index":{"A":[0,32],"set":[1,28,57,83],"partition":[2,58],"of":[3,8,15,26,30,45,72,84],"$[n]$":[4,16],"is":[5,19,37,146],"a":[6,91,132],"collection":[7],"pairwise":[9],"disjoint":[10],"nonempty":[11],"subsets":[12],"(called":[13],"blocks)":[14],"whose":[17],"union":[18,71],"$[n]$.":[20,31],"Let":[21,95],"$\\mathcal{B}(n)$":[22],"denote":[23,69,81],"the":[24,70,82],"family":[25,33],"all":[27,140],"partitions":[29],"$\\mathcal{A}":[34,144],"\\subseteq":[35],"\\mathcal{B}(n)$":[36],"said":[38],"to":[39],"be":[40],"$m$-intersecting":[41],"if":[42,143,169,172],"any":[43,56],"two":[44],"its":[46,73],"members":[47],"have":[48],"at":[49],"least":[50],"$m$":[51],"blocks":[52],"in":[53,93],"common.":[54],"For":[55],"$P":[59],"\\in":[60,67,101,112],"\\mathcal{B}(n)$,":[61],"let":[62,76],"$\\tau(P)":[63],"=":[64,78],"\\{x:":[65],"\\{x\\}":[66],"P\\}$":[68],"singletons.":[74],"Also,":[75],"$\\mu(P)":[77],"[n]":[79],"-\\tau(P)$":[80],"elements":[85],"that":[86,126,138],"do":[87],"not":[88],"appear":[89],"as":[90],"singleton":[92],"$P$.":[94],"\\begin{align*}":[96],"{\\mathcal":[97,154,161,176,181],"F}_{2t}":[98,155],"&":[99,110,157,164,178,183],"=\\left\\{P":[100,111],"\\mathcal{B}(n)\\":[102,113],":":[103,114],"\\":[104,115],"\\vert":[105,153,160],"\\mu":[106],"(P)\\vert\\leq":[107],"t\\right\\};\\\\{\\mathcal":[108],"F}_{2t+1}(i_0)":[109],"\\vert\\mu":[116],"(P)\\cap":[117],"([n]\\setminus":[118],"\\{i_0\\})\\vert\\leq":[119],"t\\right\\}.\\end{align*}":[120],"In":[121],"this":[122],"paper,":[123],"we":[124],"show":[125],"for":[127,139],"$r\\geq":[128],"3$,":[129],"there":[130],"exists":[131],"$n_0=n_0(r)$":[133],"depending":[134],"on":[135],"$r$":[136],"such":[137],"$n\\geq":[141],"n_0$,":[142],"\\subseteq\\mathcal{B}(n)$":[145],"$(n-r)$-intersecting,":[147],"then":[148],"\\[":[149,173],"|\\mathcal{A}|":[150],"\\leq":[151],"\\begin{cases}":[152,175],"\\vert,":[156,163],"\\text{if":[158,165,179,184],"$r=2t$};\\\\":[159,180],"F}_{2t+1}(1)":[162],"$r=2t+1$}.\\end{cases}\\]Moreover,":[166],"equality":[167],"holds":[168],"and":[170],"only":[171],"\\mathcal{A}=":[174],"F}_{2t},":[177],"F}_{2t+1}(i_0),":[182],"$r=2t+1$},\\end{cases}\\]for":[185],"some":[186],"$i_0\\in":[187],"[n]$.":[188]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}