Geodesic
Primeness of Generalized Parking Functions
The electronic journal of combinatorics, Tome 32 (2025) no. 4
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Classical parking functions are a generalization of permutations that appear in many combinatorial structures. Prime parking functions are indecomposable components such that any classical parking function can be uniquely described as a direct sum of prime ones. In this article, we extend the notion of primeness to three generalizations of classical parking functions: vector parking functions, $(p,q)$-parking functions, and two-dimensional vector parking functions. We study their enumeration by obtaining explicit formulas for the number of prime vector parking functions when the vector is an arithmetic progression, prime $(p,q)$-parking functions, and prime two-dimensional vector parking functions when the weight matrix is an affine transformation of the coordinates.
DOI : 10.37236/13576

Sam Armon    ; Joanne Beckford    ; Dillon Hanson    ; Naomi Krawzik    ; Olya Mandelshtam  1   ; Lucy Martinez    ; Catherine Yan 

1 University of Waterloo 
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     title = {Primeness of {Generalized} {Parking} {Functions}},
     journal = {The electronic journal of combinatorics},
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Sam Armon; Joanne Beckford; Dillon Hanson; Naomi Krawzik; Olya Mandelshtam; Lucy Martinez; Catherine Yan. Primeness of Generalized Parking Functions. The electronic journal of combinatorics, Tome 32 (2025) no. 4. doi: 10.37236/13576

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