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arxiv: 1811.06725 · v1 · pith:ESJGMOXZnew · submitted 2018-11-16 · 🧮 math.CO

Inhomogeneous Restricted Lattice Walks

Manfred Buchacher , Manuel Kauers This is my paper
classification 🧮 math.CO
keywords modelshalf-spaceinhomogeneouslatticeplanequarteralgebraicalways
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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.

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  1. Combinatorics of nondeterministic walks

    math.CO 2023-11 unverdicted novelty 6.0

    Nondeterministic walks generalize lattice paths by using set-valued steps whose reachable endpoint sets yield algebraic generating functions for bridges, excursions, and meanders on Dyck/Motzkin steps, with extensions...