{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:59Z","timestamp":1753893839140,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $S_{n}$ denote the set of permutations of $[n]=\\{1,2,\\dots, n\\}$. For a positive integer $k$, define $S_{n,k}$ to be the set of all permutations of $[n]$ with exactly $k$ disjoint cycles, i.e.,\\[ S_{n,k} = \\{\\pi \\in S_{n}: \\pi = c_{1}c_{2} \\cdots c_{k}\\},\\] where $c_1,c_2,\\dots ,c_k$ are disjoint cycles. The size of $S_{n,k}$ is $\\left [ \\begin{matrix}n\\\\ k \\end{matrix}\\right]=(-1)^{n-k}s(n,k)$, where $s(n,k)$ is the Stirling number of the first kind. A family $\\mathcal{A} \\subseteq S_{n,k}$ is said to be $t$-cycle-intersecting if any two elements of $\\mathcal{A}$ have at least $t$ common cycles. In this paper we show that, given any positive integers $k,t$ with $k\\geq t+1$, if $\\mathcal{A} \\subseteq S_{n,k}$ is $t$-cycle-intersecting and $n\\ge n_{0}(k,t)$ where $n_{0}(k,t) = O(k^{t+2})$, then \\[ |\\mathcal{A}| \\le \\left [ \\begin{matrix}n-t\\\\ k-t \\end{matrix}\\right],\\]with equality if and only if $\\mathcal{A}$ is the stabiliser of $t$ fixed points.<\/jats:p>","DOI":"10.37236\/4071","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:56:52Z","timestamp":1578704212000},"source":"Crossref","is-referenced-by-count":2,"title":["An Erd\u0151s-Ko-Rado Theorem for Permutations with Fixed Number of Cycles"],"prefix":"10.37236","volume":"21","author":[{"given":"Cheng Yeaw","family":"Ku","sequence":"first","affiliation":[]},{"given":"Kok Bin","family":"Wong","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2014,7,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i3p16\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i3p16\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:54:42Z","timestamp":1579258482000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v21i3p16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,7,25]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2014,7,3]]}},"URL":"https:\/\/doi.org\/10.37236\/4071","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2014,7,25]]},"article-number":"P3.16"}}