2019/10/22 by Mohammad Farrokhi Derakhshandeh Ghouchan, Ghouchan, Mohammad Farrokhi Derakhshandeh
Computer Science · Mathematics · #05A15 (Primary) 11B37 #11B83 (Secondary) #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.1910.09844
openalex publication_date 2019/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A lattice path inside the m× n table T is a sequence ν1,…,νk of cells such that νj+1-νj∈\(1,-1),(1,0),(1,1)\ for all j=1,…,k-1. The number of lattice paths in T from the first column to the (x,y)-cell is written into that cell. We present a precise description of the minimal linear recurrences among rows, columns, and columns sums. As a result, we obtain several formulas for the number of all lattice paths from the first column to the last column of T, that is, the nth column sum. Our methods are based on three classes of operators, which will also be studied independently.