English

On a bijection of Loehr and Remmel

Combinatorics 2026-07-27 v1

Abstract

In this expository article we review a remarkable bijection ϕn\phi_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 ϕn\phi_n, which is more direct than the original one, hence easier to compute and to work with.

Keywords

Cite

@article{arxiv.2607.24677,
  title  = {On a bijection of Loehr and Remmel},
  author = {Michele D'Adderio and Alessio Sgubin},
  journal= {arXiv preprint arXiv:2607.24677},
  year   = {2026}
}

Comments

14 pages, 11 figures, expository article