{"id":"https://openalex.org/W2075914278","doi":"https://doi.org/10.1017/s0963548311000289","title":"On <i>r</i>-Cross Intersecting Families of Sets","display_name":"On <i>r</i>-Cross Intersecting Families of Sets","publication_year":2011,"publication_date":"2011-08-18","ids":{"openalex":"https://openalex.org/W2075914278","doi":"https://doi.org/10.1017/s0963548311000289","mag":"2075914278"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548311000289","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548311000289","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/I4210136457","display_name":"Shibuya (Japan)","ror":"https://ror.org/03t1ztz45","country_code":"JP","type":"company","lineage":["https://openalex.org/I4210136457"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"PETER FRANKL","raw_affiliation_strings":["3-12-25 Shibuya, Shibuya-ku, Tokyo 150-0002, Japan (e-mail:","3-12-25 shibuya, shibuya-ku, tokyo 150-0002, japan (e-mail: peter.frankl@gmail.com)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"3-12-25 Shibuya, Shibuya-ku, Tokyo 150-0002, Japan (e-mail:","institution_ids":["https://openalex.org/I4210136457"]},{"raw_affiliation_string":"3-12-25 shibuya, shibuya-ku, tokyo 150-0002, japan (e-mail: peter.frankl@gmail.com)#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068874976","display_name":"Norihide Tokushige","orcid":"https://orcid.org/0000-0002-9487-7545"},"institutions":[{"id":"https://openalex.org/I32915989","display_name":"University of the Ryukyus","ror":"https://ror.org/02z1n9q24","country_code":"JP","type":"education","lineage":["https://openalex.org/I32915989"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"NORIHIDE TOKUSHIGE","raw_affiliation_strings":["College of Education, Ryukyu University, Nishihara, Okinawa 903-0213, Japan (e-mail:","College of education, ryukyu university, nishihara, okinawa 903-0213, japan (e-mail: hide@edu.u-ryukyu.ac.jp)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Education, Ryukyu University, Nishihara, Okinawa 903-0213, Japan (e-mail:","institution_ids":["https://openalex.org/I32915989"]},{"raw_affiliation_string":"College of education, ryukyu university, nishihara, okinawa 903-0213, japan (e-mail: hide@edu.u-ryukyu.ac.jp)#TAB#","institution_ids":["https://openalex.org/I32915989"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2134,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.86053131,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"20","issue":"5","first_page":"749","last_page":"752"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9911999702453613,"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":0.9886000156402588,"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":0.7174739241600037},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5767750144004822},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3609205186367035}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7174739241600037},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5767750144004822},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3609205186367035}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0963548311000289","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548311000289","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":[{"id":"https://openalex.org/G4545749264","display_name":"Discrete geometry and extremal combinatorics of hypergraphs","funder_award_id":"20340022","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W153370943","https://openalex.org/W1981531393","https://openalex.org/W1995680324","https://openalex.org/W2019935404","https://openalex.org/W2054050056","https://openalex.org/W2068795011","https://openalex.org/W2070725465","https://openalex.org/W2079135110","https://openalex.org/W2085573719","https://openalex.org/W2111430057","https://openalex.org/W2395767617"],"related_works":["https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W2298861036","https://openalex.org/W3148032049","https://openalex.org/W2271181815"],"abstract_inverted_index":{"Let":[0],"(":[1],"r":[2,19,34],"\u22121)":[3],"n":[4],"\u2265":[5],"rk":[6],"and":[7],"let":[8],"$\\FF_1,\\ldots,\\FF_r\\subset\\binom{[n]}k$":[9],".":[10,35,41],"Suppose":[11],"that":[12,39],"F":[13,18,25],"1":[14,30],"\u2229":[15,17],"\u22c5\u22c5\u22c5":[16],"\u2260":[20],"\u2205":[21],"holds":[22],"for":[23],"all":[24],"i":[26,28,32],"\u2208":[27],",":[29],"\u2264":[31,33],"Then":[36],"we":[37],"show":[38],"$\\prod_{i=1}^r|\\FF_i|\\leq\\binom{n-1}{k-1}^r$":[40]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":6},{"year":2013,"cited_by_count":4}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
