# Explicit Formulas for Enumeration of Lattice Paths: Basketball and the Kernel Method

@article{Banderier2019ExplicitFF, title={Explicit Formulas for Enumeration of Lattice Paths: Basketball and the Kernel Method}, author={Cyril Banderier and Christian Krattenthaler and Alan Krinik and Dmitry V. Kruchinin and Vladimir Kruchinin and David T. Nguyen and Michael Wallner}, journal={Lattice Path Combinatorics and Applications}, year={2019} }

This article deals with the enumeration of directed lattice walks on the integers with any finite set of steps, starting at a given altitude $j$ and ending at a given altitude $k$, with additional constraints such as, for example, to never attain altitude $0$ in-between. We first discuss the case of walks on the integers with steps $-h, \dots, -1, +1, \dots, +h$. The case $h=1$ is equivalent to the classical Dyck paths, for which many ways of getting explicit formulas involving Catalan-like…

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