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Peer-reviewedCC BY 4.0The Electronic Journal of Combinatorics

Bilateral Parking Procedures

  • Philippe Nadeau
Open at sourcePDFDOICite

Abstract

We introduce the class of bilateral parking procedures on the discrete line 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.

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Cite

BibTeXRIS
BibTeX
@article{nadeau2026bilateral,
  title = {{Bilateral Parking Procedures}},
  author = {Philippe Nadeau},
  journal = {The Electronic Journal of Combinatorics},
  year = {2026},
  month = oct,
  doi = {10.37236/15244},
  url = {https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p15},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Bilateral Parking Procedures
AU  - Philippe Nadeau
PY  - 2026
DA  - 2026/10/23
JO  - The Electronic Journal of Combinatorics
DO  - 10.37236/15244
UR  - https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p15
AB  - We introduce the class of bilateral parking procedures on the discrete line 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.
SN  - 1077-8926
ER  -