{"id":"https://openalex.org/W2962900860","doi":"https://doi.org/10.1017/s0963548317000062","title":"Uniform <i>s</i>-Cross-Intersecting Families","display_name":"Uniform <i>s</i>-Cross-Intersecting Families","publication_year":2017,"publication_date":"2017-03-28","ids":{"openalex":"https://openalex.org/W2962900860","doi":"https://doi.org/10.1017/s0963548317000062","mag":"2962900860"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548317000062","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548317000062","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/A5056866010","display_name":"P\u00e9ter Frankl","orcid":null},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]},{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"government","lineage":["https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"PETER FRANKL","raw_affiliation_strings":["Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary"],"affiliations":[{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary","institution_ids":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}]},{"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":["Moscow Institute of Physics and Technology, 9 Institutskiy per., 141701, Dolgoprudny, Russia","\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Station 8, 1015 Lausanne, Switzerland (e-mail:"],"affiliations":[{"raw_affiliation_string":"Moscow Institute of Physics and Technology, 9 Institutskiy per., 141701, Dolgoprudny, Russia","institution_ids":["https://openalex.org/I153845743"]},{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Station 8, 1015 Lausanne, Switzerland (e-mail:","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056866010"],"corresponding_institution_ids":["https://openalex.org/I127817813","https://openalex.org/I7597260"],"apc_list":null,"apc_paid":null,"fwci":3.0755,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.91869919,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"26","issue":"4","first_page":"517","last_page":"524"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9969000220298767,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9959999918937683,"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/cardinality","display_name":"Cardinality (data modeling)","score":0.8423922061920166},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8070234656333923},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5680014491081238},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.49505582451820374},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3368302285671234},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.06564119458198547},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05951300263404846}],"concepts":[{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.8423922061920166},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8070234656333923},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5680014491081238},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.49505582451820374},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3368302285671234},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.06564119458198547},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05951300263404846},{"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0963548317000062","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548317000062","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":4,"referenced_works":["https://openalex.org/W2019935404","https://openalex.org/W2053464741","https://openalex.org/W2552451242","https://openalex.org/W3143189643"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2002177687","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W24519920","https://openalex.org/W4253000595","https://openalex.org/W2087778462"],"abstract_inverted_index":{"In":[0,82],"this":[1,83],"paper":[2,84],"we":[3,72,85],"study":[4],"a":[5,103],"question":[6],"related":[7],"to":[8],"the":[9,23,87,111],"classical":[10],"Erd\u0151s\u2013Ko\u2013Rado":[11],"theorem,":[12],"which":[13,35],"states":[14],"that":[15,48],"any":[16,36,61],"family":[17],"of":[18,22,89,105,113],"k":[19],"-element":[20],"subsets":[21],"set":[24],"[":[25],"n":[26,32,99],"]":[27],"=":[28],"{1,.":[29],".":[30,45,81,100],".,":[31],"}":[33],"in":[34],"two":[37,49],"sets":[38],"intersect":[39],"has":[40],"cardinality":[41],"at":[42],"most":[43],"$\\binom{n-1}{k-1}$":[44],"We":[46],"say":[47],"non-empty":[50,122],"families":[51],"${\\mathcal":[52,64,69,91,94,115,118],"A},":[53],"{\\mathcal":[54],"B}\\subset":[55],"\\binom{[n]}{k}$":[56],"are":[57],"s-cross-intersecting":[58],"if,":[59],"for":[60,97,121],"A":[62,75],"\u2208":[63,68],"A}$":[65,92,116],",":[66,71],"B":[67,77],"B}$":[70,95,119],"have":[73],"|":[74,78,90,96,114,120],"\u2229":[76],"\u2265":[79],"s":[80],"determine":[86],"maximum":[88,112],"|+|":[93,117],"all":[98],"This":[101],"generalizes":[102],"result":[104],"Hilton":[106],"and":[107],"Milner,":[108],"who":[109],"determined":[110],"1-cross-intersecting":[123],"families.":[124]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-03-28T06:11:35.319607","created_date":"2019-07-30T00:00:00"}