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Simple walk in three quarter plane

Banff International Research Station for Mathematical Innovation and Discovery

In this talk, we consider the simple walk ($\textit{i.e.}$ walk with a set of steps {$\mathcal{S}=\{\text{W, N, E, S}\}$}) in the lattice plane. We constrain the walk to avoid the negative quadrant. The objective is to compute the number of paths $c(i,j;n)$ of length $n$, starting at $(0,0)$ and ending at $(i,j)$, with $\left(i\geq 0 \text{ or } j\geq 0\right)$ and $n\geq 0$. A way to achieve this goal is to cut the three quarters of the plane into two convex symmetric parts which will be three octants of the plane.

Mathematics; Combinatorics; Sequences, series, summability; Discrete mathematics

video/mp4

Author affiliation: Université de Tours

2018-03-31

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/65049

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/