# Higher Dimensional Lattice Walks: Connecting Combinatorial and Analytic Behavior

@article{Melczer2019HigherDL, title={Higher Dimensional Lattice Walks: Connecting Combinatorial and Analytic Behavior}, author={Stephen Melczer and M. Wilson}, journal={SIAM J. Discret. Math.}, year={2019}, volume={33}, pages={2140-2174} }

We consider the enumeration of walks on the non-negative lattice $\mathbb{N}^d$, with steps defined by a set $\mathcal{S} \subset \{-1, 0, 1\}^d \setminus \{\mathbf{0}\}$. Previous work in this area has established asymptotics for the number of walks in certain families of models by applying the techniques of analytic combinatorics in several variables (ACSV), where one encodes the generating function of a lattice path model as the diagonal of a multivariate rational function. Melczer and… CONTINUE READING

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