On Weary Drivers, Records of Trees, and Parking Functions
Combinatorics
2026-03-31 v4
Abstract
This work builds on the notion of record of rooted trees. We provide an alternative definition of parking functions, derive from it a record-preserving bijection between rooted trees and parking functions, and establish a join equidistribution result between a 5-tuple of statistics on rooted trees and a corresponding 5-tuple of statistics on parking functions. Some enumerative questions are also considered.
Cite
@article{arxiv.2506.22145,
title = {On Weary Drivers, Records of Trees, and Parking Functions},
author = {Adrián Lillo and Mercedes Rosas and Stefan Trandafir},
journal= {arXiv preprint arXiv:2506.22145},
year = {2026}
}
Comments
22 pages, 8 figures