{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:14Z","timestamp":1753893854449,"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>We prove in two different ways that the number of distinct prefixes of length $k$ of minimal factorisations of the $n$-cycle $(1\\ldots n)$ as a product of $n-1$ transpositions is $\\binom{n}{k+1}n^{k-1}$. Our first proof is not bijective but makes use of a correspondence between minimal factorisations and Cayley trees. The second proof consists of establishing a bijection between the set which we want to enumerate and the set of parking functions of a certain kind, which can be counted by a standard conjugation argument.<\/jats:p>","DOI":"10.37236\/4799","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:34:50Z","timestamp":1578670490000},"source":"Crossref","is-referenced-by-count":1,"title":["The Number of Prefixes of Minimal Factorisations of a Cycle"],"prefix":"10.37236","volume":"23","author":[{"given":"Thierry","family":"L\u00e9vy","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,8,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i3p35\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i3p35\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T00:17:31Z","timestamp":1579220251000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i3p35"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,8,19]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2016,7,8]]}},"URL":"https:\/\/doi.org\/10.37236\/4799","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,8,19]]},"article-number":"P3.35"}}