Lattice paths inside a table, II

2017/10/30 by Yaqubi, Daniel, Ghouchan, Mohammad Farrokhi Derakhshandeh, khademanlu, Mohamad Zamani
#FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.1711.01924

Abstract

Consider an m× n table T and latices paths ν₁,…,ν_k in T such that each step ν_i+1-ν_i=(1,1), (1,0) or (1,-1). The number of paths from the (1,i)-blank (resp. first column) to the (s,t)-blank is denoted by Dⁱ(s,t) (resp. D(s,t)). Also, the number of all paths form the first column to the las column is denoted by I_m(n). We give explicit formulas for the numbers D¹(s,t) and D(s,t).

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