{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T22:01:43Z","timestamp":1761861703066,"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>We prove an interesting fact describing the location of the roots of the generating polynomials of the numbers of derangements of length $n$, counted by their number of cycles. We then use this result to prove that if $k$ is the number of cycles of a randomly selected derangement of length $n$, then the probability that $k$ is congruent to a given $r$ modulo a given $q$ converges to $1\/q$. Finally, we generalize our results to $a$-derangements, which are permutations in which each cycle is longer than $a$.<\/jats:p>","DOI":"10.37236\/1128","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:55:48Z","timestamp":1578718548000},"source":"Crossref","is-referenced-by-count":4,"title":["On a Balanced Property of Derangements"],"prefix":"10.37236","volume":"13","author":[{"given":"Mikl\u00f3s","family":"B\u00f3na","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,11,6]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r102\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r102\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:06:46Z","timestamp":1579320406000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r102"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,11,6]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1128","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2006,11,6]]},"article-number":"R102"}}