Knight's paths towards Catalan numbers

被引：1

作者：

Baril, Jean-Luc ^{[1
]}

Ramirez, Jose L. ^{[2
]}

机构：

[1] Univ Bourgogne Franche Comte, LIB, BP 47 870, F-21078 Dijon, France

[2] Univ Nacl Colombia, Dept Matemat, Bogota, Colombia

来源：

DISCRETE MATHEMATICS | 2023年 / 346卷 / 06期

关键词：

Catalan number; Zigzag knight?s path; Generating function; DYCK PATHS;

D O I：

10.1016/j.disc.2023.113372

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.(c) 2023 Elsevier B.V. All rights reserved.

引用

页数：11

共 24 条

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