On a bijection of Loehr and Remmel

Abstract

In this expository article we review a remarkable bijection ${\varphi }_n$ due to Loehr and Remmel from the set of parking functions of size n into itself, which sends the bistatistic (dinv, area) into the bistatistic (area, pmaj). The only novelty of the present work is our definition of ${\varphi }_n$, which is more direct than the original one, hence easier to compute and to work with.

14 pages, 11 figures, expository article