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 $(i,j) \in
\mathbb{Z}^2_+$.Comment: 23 page

Kurkova, Irina

Raschel, Kilian

English

arXiv

23 pagesInternational audienceGessel'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 $(i,j) \in \mathbb{Z}^2_+$

Explicit expression for the generating function counting Gessel's walks

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