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arXiv · 1711.01924

Lattice paths inside a table, II

Daniel Yaqubi·Mohammad Farrokhi Derakhshandeh Ghouchan·Mohamad Zamani khademanlu
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Abstract

Consider an $m\times n$ table $T$ and latices paths $ν_1,\ldots,ν_k$ 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 $\mathcal{D}^i(s,t)$ (resp. $\mathcal{D}(s,t)$). Also, the number of all paths form the first column to the las column is denoted by $\mathcal{I}_m(n)$. We give explicit formulas for the numbers $\mathcal{D}^1(s,t)$ and $\mathcal{D}(s,t)$.

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Daniel Yaqubi, Mohammad Farrokhi Derakhshandeh Ghouchan, Mohamad Zamani khademanlu. 2023-05-11. Lattice paths inside a table, II. https://arxiv.org/abs/1711.01924

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