Prime parking functions on rooted trees

Transitive cycle factorizations and prime parking functions

Minimal transitive cycle factorizations and parking functions are related very closely. Using the correspondence between them, we find a bijection between minimal transitive factorizations of permutations of type (1, n − 1) and prime parking functions of length n.

Parking Functions, Empirical Processes, and the Width of Rooted Labeled Trees

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 con...

Parking functions , empirical processes , and the width of rooted labeled trees 1 Philippe Chassaing &

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 con...

4-PLACEMENT OF ROOTED TREES

A tree T of order n is called k-placement if there are k edge-disjoint copies of T into K_{n}. In this paper we prove some results about 4-placement of rooted trees.

Parking distributions on trees