{"id":"https://openalex.org/W2573556985","doi":"https://doi.org/10.1017/s0963548317000529","title":"Counting Intersecting and Pairs of Cross-Intersecting Families","display_name":"Counting Intersecting and Pairs of Cross-Intersecting Families","publication_year":2017,"publication_date":"2017-10-16","ids":{"openalex":"https://openalex.org/W2573556985","doi":"https://doi.org/10.1017/s0963548317000529","mag":"2573556985"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548317000529","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548317000529","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1701.04110","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056866010","display_name":"P\u00e9ter Frankl","orcid":null},"institutions":[{"id":"https://openalex.org/I153845743","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322","country_code":"RU","type":"education","lineage":["https://openalex.org/I153845743"]},{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH","RU"],"is_corresponding":true,"raw_author_name":"PETER FRANKL","raw_affiliation_strings":["Department of Discrete Mathematics, Moscow Institute of Physics and Technology, Moscow, Russia and Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Switzerland (e-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Discrete Mathematics, Moscow Institute of Physics and Technology, Moscow, Russia and Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Switzerland (e-mail:","institution_ids":["https://openalex.org/I5124864","https://openalex.org/I153845743"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048570599","display_name":"Andrey Kupavskii","orcid":"https://orcid.org/0000-0002-8313-9598"},"institutions":[{"id":"https://openalex.org/I153845743","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322","country_code":"RU","type":"education","lineage":["https://openalex.org/I153845743"]},{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH","RU"],"is_corresponding":false,"raw_author_name":"ANDREY KUPAVSKII","raw_affiliation_strings":["Department of Discrete Mathematics, Moscow Institute of Physics and Technology, Moscow, Russia and Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Switzerland (e-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Discrete Mathematics, Moscow Institute of Physics and Technology, Moscow, Russia and Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Switzerland (e-mail:","institution_ids":["https://openalex.org/I5124864","https://openalex.org/I153845743"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056866010"],"corresponding_institution_ids":["https://openalex.org/I153845743","https://openalex.org/I5124864"],"apc_list":null,"apc_paid":null,"fwci":1.0243,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.69661017,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"27","issue":"1","first_page":"60","last_page":"68"},"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/T11166","display_name":"Analytic Number Theory Research","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9914000034332275,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/intersection","display_name":"Intersection (aeronautics)","score":0.8472614288330078},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8049771189689636},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7102182507514954},{"id":"https://openalex.org/keywords/family-of-sets","display_name":"Family of sets","score":0.5723740458488464},{"id":"https://openalex.org/keywords/extremal-combinatorics","display_name":"Extremal combinatorics","score":0.5394149422645569},{"id":"https://openalex.org/keywords/asymptotically-optimal-algorithm","display_name":"Asymptotically optimal algorithm","score":0.41929009556770325},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08964350819587708},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.08940005302429199},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.07661652565002441},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.058724939823150635}],"concepts":[{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.8472614288330078},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8049771189689636},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7102182507514954},{"id":"https://openalex.org/C150591576","wikidata":"https://www.wikidata.org/wiki/Q739925","display_name":"Family of sets","level":3,"score":0.5723740458488464},{"id":"https://openalex.org/C549619432","wikidata":"https://www.wikidata.org/wiki/Q5422299","display_name":"Extremal combinatorics","level":2,"score":0.5394149422645569},{"id":"https://openalex.org/C181789720","wikidata":"https://www.wikidata.org/wiki/Q4812191","display_name":"Asymptotically optimal algorithm","level":2,"score":0.41929009556770325},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08964350819587708},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.08940005302429199},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07661652565002441},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.058724939823150635},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1017/s0963548317000529","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548317000529","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:real.mtak.hu:90047","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400081","display_name":"Repository of the Academy's Library (Library of the Hungarian Academy of Sciences)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210140733","host_organization_name":"Library and Information Centre of the Hungarian Academy of Sciences","host_organization_lineage":["https://openalex.org/I4210140733"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:arXiv.org:1701.04110","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1701.04110","pdf_url":"https://arxiv.org/pdf/1701.04110","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":"","raw_type":null},{"id":"mag:2573556985","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1701.04110.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:infoscience.epfl.ch:234065","is_oa":false,"landing_page_url":"http://infoscience.epfl.ch/record/234065","pdf_url":null,"source":{"id":"https://openalex.org/S4306400488","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"doi:10.48550/arxiv.1701.04110","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1701.04110","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1701.04110","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1701.04110","pdf_url":"https://arxiv.org/pdf/1701.04110","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":"","raw_type":null},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W2014910702","https://openalex.org/W2019935404","https://openalex.org/W2025247912","https://openalex.org/W2044387656","https://openalex.org/W2053464741","https://openalex.org/W2068795011","https://openalex.org/W2131713099","https://openalex.org/W2153305111","https://openalex.org/W2587992556","https://openalex.org/W3136243343","https://openalex.org/W3143189643"],"related_works":["https://openalex.org/W2963830531","https://openalex.org/W3143193920","https://openalex.org/W2962900860","https://openalex.org/W1525984693","https://openalex.org/W2952103174","https://openalex.org/W194331735","https://openalex.org/W1984685721","https://openalex.org/W2998871639","https://openalex.org/W1416598942","https://openalex.org/W2076669108","https://openalex.org/W3200318753","https://openalex.org/W2962968488","https://openalex.org/W2949993512","https://openalex.org/W2510521098","https://openalex.org/W2803507800","https://openalex.org/W3047369485","https://openalex.org/W2886252822","https://openalex.org/W2951920594","https://openalex.org/W2963037949","https://openalex.org/W3023787660"],"abstract_inverted_index":{"A":[0,20],"family":[1,39],"of":[2,4,16,36,40,43,61,64,75,110,122,133],"subsets":[3],"{1,.":[5,44,65],".":[6,45,66],".,":[7,46,67],"n":[8,47,68,88],"}":[9,69],"is":[10,125],"called":[11],"intersecting":[12,38,59,112,116],"if":[13],"any":[14],"two":[15],"its":[17],"sets":[18,124],"intersect.":[19],"classical":[21],"result":[22,74],"in":[23],"extremal":[24],"combinatorics":[25],"due":[26],"to":[27],"Erd\u0151s,":[28],"Ko":[29],"and":[30,80,95],"Rado":[31],"determines":[32],"the":[33,54,101,108,120],"maximum":[34],"size":[35],"an":[37],"k":[41,62,91,96],"-subsets":[42,63],"}.":[48],"In":[49],"this":[50,84],"paper":[51],"we":[52,82,104],"study":[53],"following":[55],"problem:":[56],"How":[57],"many":[58],"families":[60,117],"are":[70],"there?":[71],"Improving":[72],"a":[73],"Balogh,":[76],"Das,":[77],"Delcourt,":[78],"Liu":[79],"Sharifzadeh,":[81],"determine":[83,106],"quantity":[85],"asymptotically":[86,107],"for":[87,118,131],"\u2265":[89],"2":[90],"+2+2":[92],"$\\sqrt{k\\log":[93],"k}$":[94],"\u2192":[97],"\u221e.":[98],"Moreover,":[99],"under":[100],"same":[102],"assumptions":[103],"also":[105],"number":[109],"non-trivial":[111],"families,":[113],"that":[114],"is,":[115],"which":[119],"intersection":[121],"all":[123],"empty.":[126],"We":[127],"obtain":[128],"analogous":[129],"results":[130],"pairs":[132],"cross-intersecting":[134],"families.":[135]},"counts_by_year":[{"year":2017,"cited_by_count":2}],"updated_date":"2026-03-20T20:47:17.329874","created_date":"2025-10-10T00:00:00"}