Enumerating k-Naples Parking Functions Through Catalan Objects

2021/09/03 by João Pedro Carvalho de Souza, Carvalho, João Pedro, Pamela E. Harris +7 · 2 citations
Computer Science · Mathematics · #05A15 #05A19 #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2109.01735

openalex publication_date 2021/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Restricted Fubini Rankings and Restricted Unit Interval Parking Functions
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