Richard P. Stanley Seminar in Combinatorics: Some enumerative properties of parking functions and labelled forests

SEMINARS, HARVARD-MIT COMBINATORICS

Speaker:

Mei Yin - University of Denver

A parking function is a sequence (a_1,…,a_n) of positive integers such that if b_1<=…<=b_n is the increasing rearrangement of a_1,…,a_n, then b_i<=i for 1<=i<=n. Parking functions of length n are in bijection with labelled forests on the vertex set [n]={1,2,…,n} (or rooted trees on [n]_0={0,1,…,n} with root 0). We obtain some new results on the enumeration of parking functions and labelled forests, concentrating in particular on the joint distribution of several sets of statistics on parking functions. The distribution of most of these individual statistics is known, but the joint distributions are new. Extensions of our techniques are discussed. Joint work with Richard Stanley and with Stephan Wagner.

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