{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T23:14:24Z","timestamp":1768778064418,"version":"3.49.0"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Two set partitions of an $n$-set are said to $t$-intersect if they have $t$ classes in common. A $k$-partition is a set partition with $k$ classes and a $k$-partition is said to be uniform if every class has the same cardinality $c=n\/k$.  In this paper, we prove a higher order generalization of the Erd\u0151s-Ko-Rado theorem for systems of pairwise $t$-intersecting uniform $k$-partitions of an $n$-set. We prove that for $n$ large enough, any such system contains at most $${1\\over(k-t)!} {n-tc \\choose c} {n-(t+1)c \\choose c} \\cdots {n-(k-1)c \\choose c}$$ partitions and this bound is only attained by a trivially $t$-intersecting system. We also prove that for $t=1$, the result is valid for all $n$. We conclude with some conjectures on this and other types of intersecting partition systems.<\/jats:p>","DOI":"10.37236\/1937","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:10:07Z","timestamp":1578719407000},"source":"Crossref","is-referenced-by-count":9,"title":["Erd\u0151s-Ko-Rado theorems for uniform set-partition systems"],"prefix":"10.37236","volume":"12","author":[{"given":"Karen","family":"Meagher","sequence":"first","affiliation":[]},{"given":"Lucia","family":"Moura","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2005,8,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r40\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r40\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:47:53Z","timestamp":1579322873000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1r40"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,8,25]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1937","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,8,25]]},"article-number":"R40"}}