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arXiv · 0912.0457

Explicit expression for the generating function counting Gessel's walks

Irina Kurkova·Kilian Raschel
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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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Irina Kurkova, Kilian Raschel. 2010-11-18. Explicit expression for the generating function counting Gessel's walks. https://arxiv.org/abs/0912.0457

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