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The complete Generating Function for Gessel Walks is Algebraic

Abstract : Gessel walks are lattice walks in the quarter plane $\set N^2$ which start at the origin $(0,0)\in\set N^2$ and consist only of steps chosen from the set $\{\leftarrow,\swarrow,\nearrow,\to\}$. We prove that if $g(n;i,j)$ denotes the number of Gessel walks of length $n$ which end at the point $(i,j)\in\set N^2$, then the trivariate generating series $G(t;x,y)=\sum_{n,i,j\geq 0} g(n;i,j)x^i y^j t^n$ is an algebraic function.
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https://hal.inria.fr/hal-00780429
Contributor : Alin Bostan <>
Submitted on : Wednesday, January 23, 2013 - 10:14:00 PM
Last modification on : Sunday, April 26, 2020 - 1:34:02 PM

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  • HAL Id : hal-00780429, version 1
  • ARXIV : 0909.1965

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Alin Bostan, Manuel Kauers. The complete Generating Function for Gessel Walks is Algebraic. 2009. ⟨hal-00780429⟩

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