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arXiv · 2506.22145

On Weary Drivers, Records of Trees, and Parking Functions

Adrián Lillo·Mercedes Rosas·Stefan Trandafir
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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.

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Adrián Lillo, Mercedes Rosas, Stefan Trandafir. 2026-03-30. On Weary Drivers, Records of Trees, and Parking Functions. https://arxiv.org/abs/2506.22145

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