vix.ing · top · new · best · stats · spec

On Enumeration of Dyck Paths with colored hills

2018/03/21 by Milan Janjić, Janjic, Milan
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1803.07887

openalex publication_date 2018/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We continue to investigate the properties of the earlier defined functions fm and gm, which depend on an initial arithmetic function f0. In this papers values of f0 are the Fine numbers. We investigate functions fi; gi; (i = 1; 2; 3; 4). For each function, we derive an explicit formula and give a combinatorial interpretation. It appears that g2 and g3 are well-known combinatoric object called the Catalan triangles. We finish with an identity consisting of ten items.

Related