{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:36Z","timestamp":1753893816453,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $[n]=\\{1,2,\\ldots,n\\}$ and $\\mathscr{B}_n=\\{A: A\\subseteq [n]\\}$.\u00a0A family $\\mathscr{A}\\subseteq \\mathscr{B}_n$ is a Sperner family if $A\\nsubseteq B$ and $B\\nsubseteq A$ for distinct $A,B\\in\\mathscr{A}$.\u00a0Sperner's theorem states that the density of the largest Sperner family in $\\mathscr{B}_n$ is $\\binom{n}{\\left\\lceil{n\/2}\\right\\rceil}\/2^n$.\u00a0The objective of this note is to show that the same holds if $\\mathscr{B}_n$ is replaced by compressed ideals over $[n]$.<\/jats:p>","DOI":"10.37236\/5750","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:38:25Z","timestamp":1578670705000},"source":"Crossref","is-referenced-by-count":0,"title":["A Generalization of Sperner's Theorem on Compressed Ideals"],"prefix":"10.37236","volume":"23","author":[{"given":"Lili","family":"Mu","sequence":"first","affiliation":[]},{"given":"Yi","family":"Wang","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,8,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i3p24\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i3p24\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T00:17:46Z","timestamp":1579220266000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i3p24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,8,5]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2016,7,8]]}},"URL":"https:\/\/doi.org\/10.37236\/5750","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,8,5]]},"article-number":"P3.24"}}