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arXiv · 2109.01735

Enumerating $k$-Naples Parking Functions Through Catalan Objects

João Pedro Carvalho·Pamela E. Harris·Gordon Rojas Kirby·Nico Tripeny·Andrés R. Vindas-Meléndez
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Abstract

This paper studies a generalization of parking functions named $k$-Naples parking functions, where backward movement is allowed. One consequence of backward movement is that the number of ascending $k$-Naples is not the same as the number of descending $k$-Naples. This paper focuses on generalizing the bijections of ascending parking functions with combinatorial objects enumerated by the Catalan numbers in the setting of both ascending and descending $k$-Naples parking functions. These combinatorial objects include Dyck paths, binary trees, triangulations of polygons, and non-crossing partitions. Using these bijections, we enumerate both ascending and descending $k$-Naples parking functions.

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João Pedro Carvalho, Pamela E. Harris, Gordon Rojas Kirby, Nico Tripeny, Andrés R. Vindas-Meléndez. 2021-09-03. Enumerating $k$-Naples Parking Functions Through Catalan Objects. https://arxiv.org/abs/2109.01735

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