Abstract
The notions of U-parking functions and (p,q)-parking functions are two high-dimensional generalizations of the classical parking functions. U-parking functions are defined via a special family of interpolation polynomials called Gončarov polynomials, while (p,q)-parking functions can be interpreted as recurrent configurations in the sandpile model for a complete bipartite graph with an additional root, as introduced by Cori and Poulalhon. In this paper we show that (p,q)-parking functions can be obtained as a specialization of U-parking functions and characterized by a pair of weakly disjoint lattice paths in the grid p×q. Then we present various enumerative results for increasing (p,q)-parking functions.
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