{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:42Z","timestamp":1753893822157,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The goal of this work is to describe a uniform generation tree for permutations which preserves the number of $k$-cycles between any\u00a0permutation (except for a small unavoidable subset of optimal\u00a0size) of the tree and its direct children. Moreover, the tree we\u00a0describe has the property that if the number of\u00a0$k$-cycles does not change during any $k$ consecutive levels,\u00a0then any further random descent will always yield\u00a0permutations with that same number of $k$-cycles. This specific\u00a0additional property yields interesting applications for exact\u00a0sampling. We describe a new random generation algorithm for\u00a0permutations with a fixed number of $k$-cycles in $n+\\mathcal{O}(1)$\u00a0expected calls to a random integer sampler. Another application is a\u00a0combinatorial algorithm for exact sampling from the Poisson\u00a0distribution with parameter $1\/k$.<\/jats:p>","DOI":"10.37236\/6014","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T19:55:26Z","timestamp":1578686126000},"source":"Crossref","is-referenced-by-count":0,"title":["Preserving the Number of Cycles of Length $k$ in a Growing Uniform Permutation"],"prefix":"10.37236","volume":"23","author":[{"given":"Philippe","family":"Duchon","sequence":"first","affiliation":[]},{"given":"Romaric","family":"Duvignau","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,11,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i4p22\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i4p22\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:10:43Z","timestamp":1579237843000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i4p22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,11,10]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2016,10,14]]}},"URL":"https:\/\/doi.org\/10.37236\/6014","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,11,10]]},"article-number":"P4.22"}}