On Weary Drivers, Records of Trees, and Parking Functions
Adrián Lillo, Mercedes Rosas, Stefan Trandafir
Published: 2025/6/27
Abstract
This work builds on a decomposition of a Cayley tree using the notion of a record, a concept closely related to the blob encoding of a tree introduced by Kreweras and Moszkowski, and Picciotto, that we explore and extend. We provide an alternative definition of parking functions and derive from it a record-preserving bijection between Cayley trees and parking functions. Finally, we use this bijection to establish an equidistribution between a sextuple of statistics on Cayley trees and a corresponding sextuple of statistics on parking functions.