2022/03/15 by Seunghyun Seo, Seo, Seunghyun, Heesung Shin +1 · 1 citation
Engineering · Mathematics · #05A15 #05A19 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2203.07770
openalex publication_date 2022/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A lattice path is called Delannoy if its every step belongs to \N, E, D\, where N=(0,1), E=(1,0), and D=(1,1) steps. Peak, valley, and deep valley mean NE, EN, and EENN on the lattice path, respectively. In this paper, we find a bijection between Pn,m(NE, EN) and a specific subset of Pn,m(D, EENN), where Pn,m(NE, EN) is the set of Delannoy paths from the origin to the points (n,m) without peaks and valleys and Pn,m(D, EENN) is the set of Delannoy lattice paths from the origin to the points (n,m) without diagonal steps and deep valleys. We also enumerate the number of Delannoy paths without peaks and valleys on the restricted region \ (x,y) ∈ ℤ2 : y ≥ k x \ for a positive integer k.