The complete Generating Function for Gessel Walks is Algebraic - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year :

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.

Dates and versions

hal-00780429 , version 1 (23-01-2013)

Identifiers

Cite

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

Collections

INRIA INSMI INRIA2
122 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More