# Parking functions: From combinatorics to probability

@article{Kenyon2021ParkingFF, title={Parking functions: From combinatorics to probability}, author={R. Kenyon and Mei Yin}, journal={arXiv: Combinatorics}, year={2021} }

Suppose that $m$ drivers each choose a preferred parking space in a linear car park with $n$ spots. In order, each driver goes to their chosen spot and parks there if possible, and otherwise takes the next available spot if it exists. If all drivers park successfully, the sequence of choices is called a parking function. Classical parking functions correspond to the case $m=n$; we study here combinatorial and probabilistic aspects of this generalized case.
We construct a family of bijections… Expand

#### 2 Citations

Parking functions: Interdisciplinary connections

- Mathematics
- 2021

Abstract. Suppose that m drivers each choose a preferred parking space in a linear car park with n spots. In order, each driver goes to their chosen spot and parks there if possible, and otherwise… Expand

Asymptotic behaviour of the first positions of uniform parking functions

- Mathematics
- 2021

In this paper we study the asymptotic behavior of a random uniform parking function πn of size n. We show that the first kn places πn(1), . . . , πn(kn) of πn are asymptotically i.i.d. and uniform on… Expand

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