{"id":"https://openalex.org/W2531394623","doi":"https://doi.org/10.1017/s096354831900004x","title":"On the union of intersecting families","display_name":"On the union of intersecting families","publication_year":2019,"publication_date":"2019-06-27","ids":{"openalex":"https://openalex.org/W2531394623","doi":"https://doi.org/10.1017/s096354831900004x","mag":"2531394623"},"language":"en","primary_location":{"id":"doi:10.1017/s096354831900004x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s096354831900004x","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research-information.bris.ac.uk/en/publications/b9aad093-8a2e-4c69-8935-326e7eccd5bb","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"David Ellis","orcid":null},"institutions":[{"id":"https://openalex.org/I166337079","display_name":"Queen Mary University of London","ror":"https://ror.org/026zzn846","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I166337079"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"David Ellis","raw_affiliation_strings":["School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London, E1 4NS, UK"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London, E1 4NS, UK","institution_ids":["https://openalex.org/I166337079"]}]},{"author_position":"last","author":{"id":null,"display_name":"Noam Lifshitz","orcid":null},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Noam Lifshitz","raw_affiliation_strings":["Einstein Institute of Mathematics, Edmond J. Safra Campus, Hebrew University of Jerusalem, Givat Ram, Jerusalem 9190401, Israel"],"affiliations":[{"raw_affiliation_string":"Einstein Institute of Mathematics, Edmond J. Safra Campus, Hebrew University of Jerusalem, Givat Ram, Jerusalem 9190401, Israel","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I166337079"],"apc_list":null,"apc_paid":null,"fwci":0.5081,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.52060045,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"28","issue":"06","first_page":"826","last_page":"839"},"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":0.9470000267028809,"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":0.9470000267028809,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.013000000268220901,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.00930000003427267,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.607699990272522},{"id":"https://openalex.org/keywords/family-of-sets","display_name":"Family of sets","score":0.5403000116348267},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4068000018596649},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.31540000438690186},{"id":"https://openalex.org/keywords/multiple","display_name":"Multiple","score":0.26919999718666077}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7419999837875366},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6078000068664551},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.607699990272522},{"id":"https://openalex.org/C150591576","wikidata":"https://www.wikidata.org/wiki/Q739925","display_name":"Family of sets","level":3,"score":0.5403000116348267},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.475600004196167},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4068000018596649},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.31540000438690186},{"id":"https://openalex.org/C164680029","wikidata":"https://www.wikidata.org/wiki/Q1055293","display_name":"Multiple","level":2,"score":0.26919999718666077},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.2280000001192093},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.20029999315738678}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1017/s096354831900004x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s096354831900004x","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"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/b9aad093-8a2e-4c69-8935-326e7eccd5bb","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/b9aad093-8a2e-4c69-8935-326e7eccd5bb","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ellis, D C & Lifshitz, N 2019, 'On the union of intersecting families', Combinatorics, Probability and Computing. https://doi.org/10.1017/s096354831900004x","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1610.03027","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1610.03027","pdf_url":"https://arxiv.org/pdf/1610.03027","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:research-information.bris.ac.uk:publications/b9aad093-8a2e-4c69-8935-326e7eccd5bb","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1610.03027","pdf_url":null,"source":{"id":"https://openalex.org/S7407055359","display_name":"Explore Bristol Research","issn_l":null,"issn":null,"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Ellis, D C & Lifshitz, N 2019, 'On the union of intersecting families', Combinatorics, Probability and Computing. https://doi.org/10.1017/s096354831900004x","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:qmro.qmul.ac.uk:123456789/55085","is_oa":false,"landing_page_url":"https://qmro.qmul.ac.uk/xmlui/handle/123456789/55085","pdf_url":null,"source":{"id":"https://openalex.org/S4306400530","display_name":"Queen Mary Research Online (Queen Mary University of London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I166337079","host_organization_name":"Queen Mary University of London","host_organization_lineage":["https://openalex.org/I166337079"],"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":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/b9aad093-8a2e-4c69-8935-326e7eccd5bb","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/b9aad093-8a2e-4c69-8935-326e7eccd5bb","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ellis, D C & Lifshitz, N 2019, 'On the union of intersecting families', Combinatorics, Probability and Computing. https://doi.org/10.1017/s096354831900004x","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W7943539","https://openalex.org/W1991001643","https://openalex.org/W2019935404","https://openalex.org/W2027882009","https://openalex.org/W2034968281","https://openalex.org/W2045485109","https://openalex.org/W2083155064","https://openalex.org/W2094660504","https://openalex.org/W2097612342","https://openalex.org/W2100856114","https://openalex.org/W2130956934","https://openalex.org/W2153305111","https://openalex.org/W2963768244"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"A":[1],"family":[2,16,119],"of":[3,26,32,35,40,44,52,120,124,190,200],"sets":[4,13],"is":[5,89,116,183],"said":[6],"to":[7,187],"be":[8],"intersecting":[9,38,118],"if":[10,87,154],"any":[11,70,78],"two":[12],"in":[14,221],"the":[15,24,28,188,191,206,210,222,239],"have":[17],"non-empty":[18],"intersection.":[19],"In":[20],"1973,":[21],"Erd\u0151s":[22],"raised":[23],"problem":[25],"determining":[27],"maximum":[29],"possible":[30,185],"size":[31,189],"a":[33,197],"union":[34],"r":[36,59,73,180,224],"different":[37],"families":[39],"k":[41,57,121,134,145],"-element":[42,47,92,122],"subsets":[43,123],"an":[45,90,117,230],"n":[46,55,91],"set,":[48,93],"for":[49,69,77,170],"each":[50,111],"triple":[51],"integers":[53],"(":[54],",":[56,58,86,109,126,150,220],").":[60],"We":[61],"make":[62],"progress":[63],"on":[64],"this":[65],"problem,":[66],"proving":[67],"that":[68],"fixed":[71],"integer":[72],"\u2a7e":[74],"2":[75],"and":[76,94,195,202,238],"$$k":[79,213],"\\le":[80,130],"({1":[81],"\\over":[82],"2}":[83],"-":[84,139,142,216],"o(1))n$$":[85],"X":[88,125,174],"$${\\cal":[95,155],"F}":[96,156],"=":[97,157,162,179,225],"{\\cal":[98,101,106,113],"F}_1":[99],"\\cup":[100,103,105],"F}_2":[102],"\\cdots":[104],"F}_r":[107],"$$":[108,112,115,169],"where":[110],"F}_i":[114],"then":[127],"$$|{\\cal":[128],"F}|":[129],"\\left(":[131,140],"{\\matrix{n":[132],"\\cr":[133,135,144,146],"}":[136,137,147,148],"\\right)":[138],"{\\matrix{{n":[141],"r}":[143],"\\right)$$":[149],"with":[151,175],"equality":[152],"only":[153],"\\{":[158],"S":[159],"\\subset":[160],"X:|S|":[161],"k,\\;S":[163],"\\cap":[164],"R":[165,172,177],"\\ne":[166],"\\emptyset":[167],"\\}":[168],"some":[171],"\u2282":[173],"|":[176,178],".":[181],"This":[182],"best":[184],"up":[186],"o":[192],"(1)":[193],"term,":[194],"improves":[196],"1987":[198],"result":[199],"Frankl":[201],"F\u00fcredi,":[203],"who":[204],"obtained":[205],"same":[207],"conclusion":[208],"under":[209],"stronger":[211],"hypothesis":[212],"&amp;#x003C;":[214],"(3":[215],"\\sqrt":[217],"5":[218],")n/2$$":[219],"case":[223],"2.":[226],"Our":[227],"proof":[228],"utilizes":[229],"isoperimetric,":[231],"influence-based":[232],"method":[233],"recently":[234],"developed":[235],"by":[236],"Keller":[237],"authors.":[240]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2016-10-21T00:00:00"}
