# 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}
}```
• Published 21 September 2016
• Mathematics
• Lattice Path Combinatorics and Applications
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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