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Hypergeometric expressions for generating functions of walks with small steps in the quarter plane

2017
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European journal of combinatorics (Print)
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We study nearest-neighbors walks on the two-dimensional square lattice, that is, models of walks on Z 2 defined by a fixed step set that is a subset of the non-zero vectors with coordinates 0, 1 or −1. We concern ourselves with the enumeration of such walks starting at the origin and constrained to remain in the quarter plane N 2 , counted by their length and by the position of their ending point. Bousquet-Mélou and Mishna [Contemp. Math., pp. 1-39, Amer. Math. Soc., 2010] identified 19 models

doi:10.1016/j.ejc.2016.10.010
fatcat:bivi2veq6nbnvdy6jdntxa6ugi