Abstract
We present a bijection between two well-known objects in the ubiquitous Catalan family: non-decreasing parking functions and Łukasiewicz paths. This bijection maps the maximum displacement of a parking function to the height of the corresponding Łukasiewicz path, and the total displacement to the area of the path. We also study this bijection restricted to two specific families of parking functions: unit-interval parking functions and prime parking functions.
| Original language | English |
|---|---|
| Pages (from-to) | 77-84 |
| Number of pages | 8 |
| Journal | Discrete Mathematics Letters |
| Volume | 14 |
| DOIs | |
| Publication status | Published - 2024 |
Keywords
- Catalan numbers
- bijection
- displacement statistic
- parking functions
- Łukasiewicz paths