Mathematics – Combinatorics
Scientific paper
2011-01-04
Mathematics
Combinatorics
Scientific paper
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 nonholonomic, can be easily inverted, and can be used to obtain asymptotic expressions for the counting coefficients.
Adan Ivo J. B. F.
Raschel Kilian
van Leeuwaarden Johan S. H.
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