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Enumeration of planar lattice walks is a classical topic in combinatorics, at the cross-roads of several domains (e.g., probability, statistical physics, computer science).
Positive random walks and Galois theory
V. Malyshev · 1971
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Two coupled processors: the reduction to a Riemann-Hilbert problem
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J. P. C. Blanc. The relaxation time of two queueing systems in series. Comm. Statist. Stochastic Models
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Random walks in the quarter plane
G. Fayolle, R. Iasnogorodski, and V. Malyshev · 1999
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Solvability theory of boundary value problems and singular integral equations with shift
G. Litvinchuk · 2000
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M. Bousquet-Mélou, and M., Petkovsek. Walks confined in a quadrant are not always D-finite. Theoret. Comput. Sci
2003
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A. Bostan, and M. Kauers. Automatic classification of restricted lattice walks. Proceedings of the 21 21 st International Conference on Formal Power Series and Algebraic Combinatorics
2009
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Analytic Combinatorics
P. Flajolet, and R. Sedgewick · 2009
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M. Mishna, and A. Rechnitzer. Two non-holonomic lattice walks in the quarter plane. Theor. Comput. Sci
2009
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The complete generating function for Gessel’s walk is algebraic
On the holonomy or algebraicity of generating functions counting lattice walks in the quarter plane
G. Fayolle, and K. Raschel · 2010
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D. Denisov, and V. Wachtel. Random walks in cones. Preprint
2011
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Random walks in the quarter-plane with zero drift: an explicit criterion for the finiteness of the associated group
G. Fayolle, and K. Raschel · 2011
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Random walks in ℤ + 2 \mathbb{Z}_{+}^{2} with non-zero drift absorbed at the axes
I. Kurkova, and K. Raschel · 2011
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On the functions counting walks with small steps in the quarter plane
I. Kurkova, and K. Raschel · 2011
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G. Fayolle, and K. Raschel. Some exact asymptotics in the counting of walks in the quarter plane (extended version). In preparation
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A. Bostan, and M. Kauers · 2010
Cited alongside, same era.
M. Bousquet-Mélou, and M. Mishna. Walks with small steps in the quarter plane. Contemp. Math
2010
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A. Bostan, and M. Kauers. Unpublished notes
Cited in the paper.
2012
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K. Raschel. Counting walks in a quadrant: a unified approach via boundary value problems. J. Eur. Math. Soc
2012
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