The complete Generating Function for Gessel Walks is Algebraic
نویسندگان
چکیده
Gessel walks are lattice walks in the quarter plane N2 which start at the origin (0, 0) ∈ N2 and consist only of steps chosen from the set {←,↙,↗,→}. We prove that if g(n; i, j) denotes the number of Gessel walks of length n which end at the point (i, j) ∈ N2, then the trivariate generating series G(t;x, y) = X n,i,j≥0 g(n; i, j)xyt is an algebraic function.
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عنوان ژورنال:
- CoRR
دوره abs/0909.1965 شماره
صفحات -
تاریخ انتشار 2009