{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:24:07Z","timestamp":1759335847020,"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>This paper provides tight bounds for the moments of the width of rooted labeled trees with $n$ nodes, answering an open question of Odlyzko and Wilf (1987). To this aim, we use  one of the many one-to-one correspondences between trees and parking functions, and also a precise coupling between parking functions and the empirical processes of mathematical statistics. Our result turns out to be a consequence  of  the strong convergence of  empirical processes to the Brownian bridge (Koml\u00f3s, Major and Tusn\u00e1dy, 1975).<\/jats:p>","DOI":"10.37236\/1558","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:09:06Z","timestamp":1578708546000},"source":"Crossref","is-referenced-by-count":22,"title":["Parking Functions, Empirical Processes, and the Width of Rooted Labeled Trees"],"prefix":"10.37236","volume":"8","author":[{"given":"Philippe","family":"Chassaing","sequence":"first","affiliation":[]},{"given":"Jean-Fran\u00e7ois","family":"Marckert","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2001,2,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r14\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r14\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:20:03Z","timestamp":1579324803000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v8i1r14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,2,8]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2001,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1558","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2001,2,8]]},"article-number":"R14"}}