{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:07Z","timestamp":1753893787886,"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>If we compose sufficiently many random functions on a finite set, then the  composite function will  be constant. We determine the number of compositions that are needed, on average. Choose random functions $f_1, f_2,f_3,\\dots $ independently and uniformly from among the $n^n$ functions from $[n]$ into $[n]$. For $t&gt;1$, let $g_t=f_t\\circ f_{t-1}\\circ \\cdots \\circ f_1$ be the composition of the first $t$ functions. Let $T$ be the smallest $t$ for which $g_t$ is constant(i.e. $g_t(i)=g_t(j)$ for all $i,j$). We prove that $E(T)\\sim 2n$ as $n\\rightarrow\\infty$, where $E(T)$ denotes the expected value of $T$.<\/jats:p>","DOI":"10.37236\/1642","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:25:35Z","timestamp":1578709535000},"source":"Crossref","is-referenced-by-count":6,"title":["Compositions of Random Functions on a Finite Set"],"prefix":"10.37236","volume":"9","author":[{"given":"Avinash","family":"Dalal","sequence":"first","affiliation":[]},{"given":"Eric","family":"Schmutz","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2002,7,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i1r26\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i1r26\/comment","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i1r26\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:13:45Z","timestamp":1579324425000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v9i1r26"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,7,9]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2002,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1642","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2002,7,9]]},"article-number":"R26"}}