# 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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Journal articles
Advances in Applied Mathematics, Elsevier, 2011, 47, pp.414-433
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https://hal.archives-ouvertes.fr/hal-00438190
Contributor : Kilian Raschel <>
Submitted on : Thursday, November 18, 2010 - 2:10:06 PM
Last modification on : Monday, May 29, 2017 - 2:22:57 PM
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• HAL Id : hal-00438190, version 3

### Citation

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

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