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Journal Articles Advances in Applied Mathematics Year : 2011

Explicit expression for the generating function counting Gessel's walks

Abstract

Gessel's walks are the planar walks that move within the positive quadrant $\mathbb{Z}_{+}^{2}$ by unit steps in any of the following directions: West, North-East, East and South-West. In this paper, we find an explicit expression for the trivariate generating function counting the Gessel's walks with $k\geq 0$ steps, which start at $(0,0)$ and end at a given point $(i,j) \in \mathbb{Z}^2_+$.
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Dates and versions

hal-00438190 , version 1 (02-12-2009)
hal-00438190 , version 2 (06-03-2010)
hal-00438190 , version 3 (18-11-2010)

Identifiers

  • HAL Id : hal-00438190 , version 3

Cite

Irina Kurkova, Kilian Raschel. Explicit expression for the generating function counting Gessel's walks. Advances in Applied Mathematics, 2011, 47, pp.414-433. ⟨hal-00438190v3⟩
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