Enumeration of (p, q)-parking functions

Authors:
Robert Cori;Dominique Poulalhon
Affiliations:
Labri, Université Bordeaux 1, 33405 Talence Cedex, France and LIX, École polytechnique, 91128 Palaiseau Cedex, France;LIX, École polytechnique, 91128 Palaiseau Cedex, France
Venue:
Discrete Mathematics
Year:
2002

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Abstract

Parking functions are central in many aspects of combinatorics. We define in this communication a generalization of parking functions which we call (p1,..., pk)-parking functions. We give a characterization of them in terms of parking functions and we show that they can be interpreted as recurrent configurations in the sandpile model for some graphs. We also establish a correspondence with a Lukasiewicz language, which enables to enumerate (p1,..., pk)-parking functions as well as increasing ones.