{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:06Z","timestamp":1753893786739,"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>Let $m$ be a positive integer, and $p_n(m)$ the proportion of permutations of the symmetric group $S_n$ that admit an $m$-th root. Calculating the exponential generating function of these permutations, we show the following asymptotic formula $$p_n(m)\\, \\sim \\,  {{\\pi _m}\\over {n^{1-\\varphi (m)\/m}}},\\;\\; n\\to \\infty ,$$ where $\\varphi$ is the Euler function and $\\pi _m$ an explicit constant.<\/jats:p>","DOI":"10.37236\/1620","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:27:35Z","timestamp":1578691655000},"source":"Crossref","is-referenced-by-count":7,"title":["On the Number of Permutations Admitting an m-th Root"],"prefix":"10.37236","volume":"9","author":[{"given":"Nicolas","family":"Pouyanne","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2001,12,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i1r3\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v9i1r3\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T00:16:15Z","timestamp":1579306575000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v9i1r3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,12,20]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2002,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1620","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2001,12,20]]},"article-number":"R3"}}