Knight's paths towards Catalan numbers
Combinatorics
2023-02-01 v2
Abstract
We provide enumerating results for partial knight's paths of a given size. We prove algebraically that zigzag knight's paths of a given size ending on the -axis are enumerated by the generalized Catalan numbers, and we give a constructive bijection with peakless Motzkin paths of a given length. After enumerating partial knight's paths of a given length, we prove that zigzag knight's paths of a given length ending on the -axis are counted by the Catalan numbers. Finally, we give a constructive bijection with Dyck paths of a given length.
Keywords
Cite
@article{arxiv.2206.12087,
title = {Knight's paths towards Catalan numbers},
author = {Jean-Luc Baril and José Luis Ramirez},
journal= {arXiv preprint arXiv:2206.12087},
year = {2023}
}