{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:21Z","timestamp":1753893801176,"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>Erd\u0151s posed the problem of how many random subsets need to be chosen from a set of $n$ elements, each element appearing in each subset with probability $p=1\/2$, in order that at least one subset is contained in  another. R\u00e9nyi answered this question, but could not determine the  limiting probability distribution for the number of subset counts because the higher moments diverge to infinity. The model considered by R\u00e9nyi with $p$ arbitrary is denoted by ${\\cal P}(m,n,p)$, where $m$ is the number of random subsets chosen. We give a necessary and sufficient condition on $p(n)$ and $m(n)$ for subset counts to be asymptotically Poisson and find rates of convergence using Stein's method.  We discuss how Poisson limits can be shown for other statistics of ${\\cal P}(m,n,p)$.<\/jats:p>","DOI":"10.37236\/1812","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:32:17Z","timestamp":1578691937000},"source":"Crossref","is-referenced-by-count":0,"title":["Convergence in Distribution for Subset Counts Between Random Sets"],"prefix":"10.37236","volume":"11","author":[{"given":"Dudley","family":"Stark","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2004,9,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r59\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r59\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:54:14Z","timestamp":1579305254000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i1r59"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,9,9]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2004,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/1812","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2004,9,9]]},"article-number":"R59"}}