Knight's paths towards Catalan numbers |
| |
Institution: | 1. LIB, Université de Bourgogne Franche-Comté, B.P. 47 870, 21078 Dijon Cedex France;2. Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia |
| |
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 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. |
| |
Keywords: | Catalan number Zigzag knight's path Generating function |
本文献已被 ScienceDirect 等数据库收录! |
|