The Electronic Journal of Combinatorics· 2026Q1
Bilateral Parking Procedures
- 0citations
- Q1SCImago
- 2026year
Short summary
A new class of bilateral parking procedures, allowing cars to park left or right, yields $(r+1)^{r-1}$ parking functions for a subclass of local rules.
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Key points
- Introduced bilateral parking procedures allowing parking to the left on the discrete line $\mathbb{Z}$.
- Demonstrated that a subclass of local bilateral procedures results in $(r+1)^{r-1}$ parking functions of length $r$.
- Extended the framework to probabilistic parking decisions.
- Established a connection between bilateral procedures and labeled binary forests for combinatorial analysis.
AI-generated from the title and abstract; the full text is not read.
Abstract
We introduce the class of bilateral parking procedures on the discrete line $\mathbb{Z}$. While cars try to park in the nearest available spot to their right in the classical case, we consider more general parking rules that allow cars to use the nearest available spot to their left. We show that for a natural subclass of local procedures, the number of corresponding parking functions of length $r$ is always equal to $(r+1)^{r-1}$. The setting can be extended to probabilistic procedures, in which the decision to park left or right is random. We finally describe how bilateral procedures can naturally be encoded by certain labeled binary forests, whose combinatorics shed light on several results from the literature.
The authors' abstract, as published at the source. The Electronic Journal of Combinatorics, 2026 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics