{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T16:02:32Z","timestamp":1762444952657,"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 let $\\rho(m,n)$ be the proportion of permutations of the symmetric group $\\mathrm{Sym}(n)$ whose order is coprime to $m$. In 2002, Pouyanne proved that $\\rho(n,m)n^{1-\\frac{\\phi(m)}{m}}\\sim \\kappa_m$ where $\\kappa_m$ is a complicated (unbounded) function of $m$. We show that there exists a positive constant $C(m)$ such that, for all $n \\geq m$,\\[C(m) \\left(\\frac{n}{m}\\right)^{\\frac{\\phi(m)}{m}-1} \\leq \\rho(n,m) \\leq \\left(\\frac{n}{m}\\right)^{\\frac{\\phi(m)}{m}-1}\\]where $\\phi$ is Euler's totient function.<\/jats:p>","DOI":"10.37236\/8678","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T05:58:13Z","timestamp":1578635893000},"source":"Crossref","is-referenced-by-count":3,"title":["Permutations with Orders Coprime to a Given Integer"],"prefix":"10.37236","volume":"27","author":[{"given":"John","family":"Bamberg","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S. P.","family":"Glasby","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Scott","family":"Harper","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cheryl E.","family":"Praeger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,1,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p6\/7991","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p6\/7991","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T03:59:20Z","timestamp":1579233560000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i1p6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,10]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/8678","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,1,10]]},"article-number":"P1.6"}}