{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T18:20:25Z","timestamp":1787509225067,"version":"build-2736575974"},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2013,5,9]],"date-time":"2013-05-09T00:00:00Z","timestamp":1368057600000},"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":[[2013,7]]},"abstract":"<jats:p>\n                    Let\n                    <jats:italic>m<\/jats:italic>\n                    ,\n                    <jats:italic>n<\/jats:italic>\n                    and\n                    <jats:italic>t<\/jats:italic>\n                    be positive integers. Consider [\n                    <jats:italic>m<\/jats:italic>\n                    ]\n                    <jats:sup>\n                      <jats:italic>n<\/jats:italic>\n                    <\/jats:sup>\n                    as the set of sequences of length\n                    <jats:italic>n<\/jats:italic>\n                    on an\n                    <jats:italic>m<\/jats:italic>\n                    -letter alphabet. We say that two subsets\n                    <jats:italic>A<\/jats:italic>\n                    \u2282[\n                    <jats:italic>m<\/jats:italic>\n                    ]\n                    <jats:sup>\n                      <jats:italic>n<\/jats:italic>\n                    <\/jats:sup>\n                    and\n                    <jats:italic>B<\/jats:italic>\n                    \u2282[\n                    <jats:italic>m<\/jats:italic>\n                    ]\n                    <jats:sup>\n                      <jats:italic>n<\/jats:italic>\n                    <\/jats:sup>\n                    cross\n                    <jats:italic>t<\/jats:italic>\n                    -intersect if any two sequences\n                    <jats:italic>a<\/jats:italic>\n                    \u2208\n                    <jats:italic>A<\/jats:italic>\n                    and\n                    <jats:italic>b<\/jats:italic>\n                    \u2208\n                    <jats:italic>B<\/jats:italic>\n                    match in at least\n                    <jats:italic>t<\/jats:italic>\n                    positions. In this case it is shown that if\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0963548313000138_inline1\"\/>\n                        <jats:tex-math>$m &gt; (1-\\frac 1{\\sqrt[t]2})^{-1}$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    then |\n                    <jats:italic>A<\/jats:italic>\n                    ||\n                    <jats:italic>B<\/jats:italic>\n                    |\u2264(\n                    <jats:italic>m<\/jats:italic>\n                    <jats:sup>\n                      <jats:italic>n\u2212t<\/jats:italic>\n                    <\/jats:sup>\n                    )\n                    <jats:sup>2<\/jats:sup>\n                    . We derive this result from a weighted version of the Erd\u0151s\u2013Ko\u2013Rado theorem concerning cross\n                    <jats:italic>t<\/jats:italic>\n                    -intersecting families of subsets, and we also include the corresponding stability statement. One of our main tools is the eigenvalue method for intersection matrices due to Friedgut [10].\n                  <\/jats:p>","DOI":"10.1017\/s0963548313000138","type":"journal-article","created":{"date-parts":[[2013,5,9]],"date-time":"2013-05-09T05:05:30Z","timestamp":1368075930000},"page":"622-637","source":"Crossref","is-referenced-by-count":9,"title":["Cross\n                    <i>t<\/i>\n                    -Intersecting Integer Sequences from Weighted Erd\u0151s\u2013Ko\u2013Rado"],"prefix":"10.1017","volume":"22","author":[{"given":"NORIHIDE","family":"TOKUSHIGE","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2013,5,9]]},"reference":[{"key":"S0963548313000138_ref16","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579226"},{"key":"S0963548313000138_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-008-2318-9"},{"key":"S0963548313000138_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(86)90063-4"},{"key":"S0963548313000138_ref7","unstructured":"Frankl P. , Lee S. J. , Siggers M. and Tokushige N. An Erd\u0151s\u2013Ko\u2013Rado theorem for cross t-intersecting families. arXiv:1303.0657"},{"key":"S0963548313000138_ref5","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/12.1.313"},{"key":"S0963548313000138_ref4","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-2011-00690-5"},{"key":"S0963548313000138_ref3","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2005.162.439"},{"key":"S0963548313000138_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/s00039-010-0073-8"},{"key":"S0963548313000138_ref15","article-title":"The eigenvalue method for cross t-intersecting families","author":"Tokushige","journal-title":"J. Alg. Combin."},{"key":"S0963548313000138_ref6","doi-asserted-by":"publisher","DOI":"10.1137\/0601044"},{"key":"S0963548313000138_ref14","first-page":"89","article-title":"Intersecting families: Uniform versus weighted","volume":"18","author":"Tokushige","year":"2005","journal-title":"Ryukyu Math. J."},{"key":"S0963548313000138_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-6048-4_5"},{"key":"S0963548313000138_ref1","doi-asserted-by":"publisher","DOI":"10.1006\/aama.1998.0588"},{"key":"S0963548313000138_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(66)80012-1"},{"key":"S0963548313000138_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s004930050045"},{"key":"S0963548313000138_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(89)90065-4"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548313000138","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,23]],"date-time":"2019-04-23T17:15:20Z","timestamp":1556039720000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548313000138\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,5,9]]},"references-count":16,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2013,7]]}},"alternative-id":["S0963548313000138"],"URL":"https:\/\/doi.org\/10.1017\/s0963548313000138","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,5,9]]}}}