{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:42:53Z","timestamp":1753893773828,"version":"3.41.2"},"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>The lattice of the set partitions of $[n]$ ordered by refinement is studied. Suppose $r$ partitions $p_1,\\dots,p_r$ are chosen independently and uniformly at random. The probability that the coarsest refinement of all $p_i$'s is the finest partition $\\bigl\\{\\{1\\},\\dots,\\{n\\}\\bigr\\}$ is shown to approach $0$ for $r=2$, and $1$ for $r\\ge 3$. The probability that the finest coarsening of all $p_i$'s is the one-block partition is shown to approach $1$ for every $r\\ge 2$.<\/jats:p>","DOI":"10.37236\/1483","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:05:42Z","timestamp":1578708342000},"source":"Crossref","is-referenced-by-count":9,"title":["Where the Typical Set Partitions Meet and Join"],"prefix":"10.37236","volume":"7","author":[{"given":"Boris","family":"Pittel","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2000,1,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r5\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:25:24Z","timestamp":1579325124000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v7i1r5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,1,15]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2000,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1483","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2000,1,15]]},"article-number":"R5"}}