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Séminaire Lotharingien de Combinatoire, 82B.75 (2019), 12 pp.

# Manfred Buchacher and Manuel Kauers

# Inhomogeneous restricted lattice walks

**Abstract.**
We consider inhomogeneous lattice walk models in a half-space and in the quarter plane. For the models in a half-space, we show by a generalization of the kernel method to linear systems of functional equations that their generating functions are always algebraic. For the models in the quarter plane, we have carried out an experimental classification of all models with small steps. We discovered many (apparently) D-finite cases for most of which we have no explanation yet.

Received: November 15, 2018.
Accepted: February 17, 2019.
Final version: April 1, 2019.

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