2022/06/24 by Jean-Luc Baril, Baril, Jean-Luc, José Luis Ramirez +1
Mathematics · #Advanced Combinatorial Mathematics #Mathematics and Applications #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2206.12087
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 x-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 x-axis are counted by the Catalan numbers. Finally, we give a constructive bijection with Dyck paths of a given length.