Parking functions and Łukasiewicz paths

Research output: Other contribution


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 maximal 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 languageEnglish
TypeArXiv preprint
Media of outputArXiv
Number of pages11
Publication statusPublished - 27 Mar 2024


  • Parking functions
  • Łukasiewicz paths
  • Catalan numbers
  • Displacement statistic
  • Bijection

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