The complete generating function for Gessel walks is algebraic
نویسندگان
چکیده
منابع مشابه
The complete Generating Function for Gessel Walks is Algebraic
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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Article history: Received 13 December 2009 Accepted 29 September 2010 Available online 3 December 2010 MSC: primary 05A15 secondary 30F10, 30D05
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2010
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-2010-10398-2