{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T17:55:02Z","timestamp":1778522102775,"version":"3.51.4"},"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>A Sperner partition system is a system of set partitions such that any two set partitions $P$ and $Q$ in the system have the property that for all classes $A$ of $P$ and all classes $B$ of $Q$, $A \\not\\subseteq B$ and $B \\not\\subseteq A$.  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 Sperner's Theorem. In particular, we show that if $k$ divides $n$ the largest Sperner $k$-partition system on an $n$-set has cardinality ${n-1 \\choose n\/k-1}$ and is a uniform partition system. We give a bound on the cardinality of a Sperner $k$-partition system of an $n$-set for any $k$ and $n$.<\/jats:p>","DOI":"10.37236\/1987","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:09:05Z","timestamp":1578719345000},"source":"Crossref","is-referenced-by-count":6,"title":["A Sperner-Type Theorem for Set-Partition Systems"],"prefix":"10.37236","volume":"12","author":[{"given":"Karen","family":"Meagher","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lucia","family":"Moura","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Brett","family":"Stevens","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2005,10,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1n20\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1n20\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:40:19Z","timestamp":1579322419000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1n20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,10,31]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1987","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,10,31]]},"article-number":"N20"}}