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- W4300565274 abstract "In two recent works cite{BMM,BK}, it has been shown that the counting generating functions (CGF) for the 23 walks with small steps confined in a quadrant and associated with a finite group of birational transformations are holonomic, and even algebraic in 4 cases -- in particular for the so-called Gessel's walk. It turns out that the type of functional equations satisfied by these CGF appeared in a probabilistic context almost 40 years ago. Then a method of resolution was proposed in cite{FIM}, involving at once algebraic tools and a reduction to boundary value problems. Recently this method has been developed in a combinatorics framework in cite{Ra}, where a thorough study of the explicit expressions for the CGF is proposed. The aim of this paper is to derive the nature of the bivariate CGF by a direct use of some general theorems given in cite{FIM}." @default.
- W4300565274 created "2022-10-03" @default.
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- W4300565274 date "2010-04-10" @default.
- W4300565274 modified "2023-10-18" @default.
- W4300565274 title "On the Holonomy or Algebraicity of Generating Functions Counting Lattice Walks in the Quarter-Plane" @default.
- W4300565274 doi "https://doi.org/10.48550/arxiv.1004.1733" @default.
- W4300565274 hasPublicationYear "2010" @default.
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