On Weary Drivers, Records of Trees, and Parking Functions

2025/06/27 by Adrián Lillo, Lillo, Adrián, Mercedes Rosas +3 · 1 citation
Computer Science · Mathematics · #05A05 (Secondary) #05A19 (Primary) 05E05 #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2506.22145

openalex publication_date 2025/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On the Lucky and Displacement Statistics of Stirling Permutations
• Some enumerative properties of parking functions
• Probabilistic Parking Functions
• Parking functions: From combinatorics to probability
• Parking Functions: Choose Your Own Adventure
• How to encode a tree
• Probabilizing Parking Functions

Cited by

• On the enumeration of records of rooted trees and rooted forests

Related

• A New Bijection Between Forests and Parking Functions
• Bijection: Parking-like structures and Tree-like structures
• Parking functions: From combinatorics to probability
• Distribution of new statistics of parking functions and their generalizations
• Parking functions for trees and mappings