Title : ( Perfect Lattice Paths in the Plane )
Authors: Daniel Yaqubi , Abbas Jafarzadeh ,
Full TextAbstract
Consider an $m\times n$ table $T$ and latices paths $\nu_1,\ldots,\nu_k$ in $T$ such that each step $\nu_{i+1}-\nu_i=(1,1)$, $(1,0)$ or $(1,-1)$. The number of paths from the $(1,i)$-cell (resp. first column) to the $(s,t)$-cell is denoted by $\D^i(s,t)$ (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 $\D^1(s,t)$ and $\D(s,t)$.
Keywords
, Lattice path, Dyck path, Perfect lattice paths, Fibonacci numbers, Pell-Lucas numbers, Motzkin numbers
@inproceedings{paperid:1066977,
author = {Daniel Yaqubi and Jafarzadeh, Abbas},
title = {Perfect Lattice Paths in the Plane},
booktitle = {دهمین کنفرانس نظریه گراف و ترکیبیات جبری},
year = {2018},
location = {یزد, IRAN},
keywords = {Lattice path; Dyck path; Perfect lattice paths; Fibonacci numbers; Pell-Lucas numbers; Motzkin numbers},
}
%0 Conference Proceedings
%T Perfect Lattice Paths in the Plane
%A Daniel Yaqubi
%A Jafarzadeh, Abbas
%J دهمین کنفرانس نظریه گراف و ترکیبیات جبری
%D 2018
