{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,23]],"date-time":"2025-09-23T13:34:04Z","timestamp":1758634444787,"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>This paper develops an analogy between the cycle structure of, on the one hand, random permutations with cycle lengths restricted to lie in an infinite set $S$ with asymptotic density $\\sigma$ and, on the other hand, permutations selected according to the Ewens distribution with parameter $\\sigma$.  In particular we show that the asymptotic expected number of cycles of random permutations of $[n]$ with all cycles even, with all cycles odd, and chosen from the Ewens distribution with parameter $1\/2$ are all ${1 \\over 2} \\log n + O(1)$, and the variance is of the same order.  Furthermore, we show that in permutations of $[n]$ chosen from the Ewens distribution with parameter $\\sigma$, the probability of a random element being in a cycle longer than $\\gamma n$ approaches $(1-\\gamma)^\\sigma$ for large $n$. The same limit law holds for permutations with cycles carrying multiplicative weights with average $\\sigma$.  We draw parallels between the Ewens distribution and the asymptotic-density case and explain why these parallels should exist using permutations drawn from weighted Boltzmann distributions.<\/jats:p>","DOI":"10.37236\/188","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:27:37Z","timestamp":1578716857000},"source":"Crossref","is-referenced-by-count":9,"title":["Profiles of Permutations"],"prefix":"10.37236","volume":"16","author":[{"given":"Michael","family":"Lugo","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,8,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r99\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r99\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T02:41:56Z","timestamp":1579315316000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r99"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,8,7]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/188","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,8,7]]},"article-number":"R99"}}