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Pré-Publication, Document De Travail Année : 2011

The compensation approach for walks with small steps in the quarter plane

Résumé

This paper is the first application of the compensation approach to counting problems. We discuss how this method can be applied to a general class of walks in the quarter plane $Z_{+}^{2}$ with a step set that is a subset of $\{(-1,1),(-1,0),(-1,-1),(0,-1),(1,-1)\}$ in the interior of $Z_{+}^{2}$. We derive an explicit expression for the counting generating function, which turns out to be meromorphic and onholonomic, can be easily inverted, and can be used to obtain asymptotic expressions for the counting coefficients.
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Dates et versions

hal-00551472 , version 1 (03-01-2011)
hal-00551472 , version 2 (07-10-2012)
hal-00551472 , version 3 (04-07-2013)

Identifiants

  • HAL Id : hal-00551472 , version 1

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Ivo Adan, Johan van Leeuwaarden, Kilian Raschel. The compensation approach for walks with small steps in the quarter plane. 2011. ⟨hal-00551472v1⟩
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