{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:39Z","timestamp":1753893819650,"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>A permutation $a_1a_2\\ldots a_n$ is indecomposable if there does not exist $p&lt;n$ such that $a_1a_2\\ldots a_p$ is a permutation of $\\{ 1,2,\\ldots,p\\}$. We consider the\u00a0 probability that a permutation of ${\\mathbb S}_n$\u00a0 with $m$ cycles is indecomposable and prove that\u00a0 this probability is monotone non-increasing in $n$.We compute\u00a0 also the asymptotic probability when\u00a0 $n$ goes to infinity with $m\/n$ tending to a fixed ratio.\u00a0 The asymptotic probability is monotone in $m\/n$, and there is no threshold phenomenon: it degrades gracefully from 1 to 0. When $n=2m$, a slight majority ($51.117\\ldots$ percent) of the permutations are indecomposable.<\/jats:p>","DOI":"10.37236\/2071","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:31:15Z","timestamp":1578713475000},"source":"Crossref","is-referenced-by-count":3,"title":["On the Number of Indecomposable Permutations with a Given Number of Cycles"],"prefix":"10.37236","volume":"19","author":[{"given":"Robert","family":"Cori","sequence":"first","affiliation":[]},{"given":"Claire","family":"Mathieu","sequence":"additional","affiliation":[]},{"given":"John Michael","family":"Robson","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2012,2,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i1p49\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i1p49\/4141","content-type":"application\/x-gzip","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i1p49\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:41:30Z","timestamp":1579300890000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i1p49"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2,29]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2012,2,15]]}},"URL":"https:\/\/doi.org\/10.37236\/2071","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,2,29]]},"article-number":"P49"}}