{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T17:30:04Z","timestamp":1778693404775,"version":"3.51.4"},"reference-count":10,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2011,8,18]],"date-time":"2011-08-18T00:00:00Z","timestamp":1313625600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2011,9]]},"abstract":"<jats:p>Let (<jats:italic>r<\/jats:italic>\u22121)<jats:italic>n<\/jats:italic> \u2265 <jats:italic>rk<\/jats:italic> and let <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548311000289_inline1\"><jats:alt-text>$\\FF_1,\\ldots,\\FF_r\\subset\\binom{[n]}k$<\/jats:alt-text><\/jats:inline-graphic>. Suppose that <jats:italic>F<\/jats:italic><jats:sub>1<\/jats:sub> \u2229 \u22c5\u22c5\u22c5 \u2229 <jats:italic>F<\/jats:italic><jats:sub><jats:italic>r<\/jats:italic><\/jats:sub> \u2260 \u2205 holds for all <jats:italic>F<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub> \u2208 <jats:private-char><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548311000289_char1\"\/><\/jats:private-char><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>, 1 \u2264 <jats:italic>i<\/jats:italic> \u2264 <jats:italic>r<\/jats:italic>. Then we show that <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0963548311000289_inline2\"><jats:alt-text>$\\prod_{i=1}^r|\\FF_i|\\leq\\binom{n-1}{k-1}^r$<\/jats:alt-text><\/jats:inline-graphic>.<\/jats:p>","DOI":"10.1017\/s0963548311000289","type":"journal-article","created":{"date-parts":[[2011,8,18]],"date-time":"2011-08-18T10:19:13Z","timestamp":1313662753000},"page":"749-752","source":"Crossref","is-referenced-by-count":17,"title":["On <i>r<\/i>-Cross Intersecting Families of Sets"],"prefix":"10.1017","volume":"20","author":[{"given":"PETER","family":"FRANKL","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"NORIHIDE","family":"TOKUSHIGE","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2011,8,18]]},"reference":[{"key":"S0963548311000289_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579279"},{"key":"S0963548311000289_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01904851"},{"key":"S0963548311000289_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(76)90073-X"},{"key":"S0963548311000289_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-005-0036-0"},{"key":"S0963548311000289_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(89)90065-4"},{"key":"S0963548311000289_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(91)90075-U"},{"key":"S0963548311000289_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(86)90025-7"},{"key":"S0963548311000289_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2009.10.010"},{"key":"S0963548311000289_ref4","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/12.1.313"},{"key":"S0963548311000289_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-004-0598-4"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548311000289","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T06:33:26Z","timestamp":1556346806000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548311000289\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,8,18]]},"references-count":10,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2011,9]]}},"alternative-id":["S0963548311000289"],"URL":"https:\/\/doi.org\/10.1017\/s0963548311000289","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,8,18]]}}}