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arXiv · 2312.08273

Staircase graph words

Sela Fried·Toufik Mansour
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Abstract

Generalizing the notion of staircase words, introduced by Knopfmacher et.\ al, we define staircase graph words. These are functions $w$ from the vertex set $V$ of a graph into the set $\{1,2,\ldots,k\}$, such that $|w(x)-w(y)|\leq 1$, for every adjacent $x,y\in V$. We find the explicit generating functions for the number of staircase graph words for the grid graph, the rectangle-triangular graph and the king's graph, all of size $2\times n$.

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Sela Fried, Toufik Mansour. 2023-12-13. Staircase graph words. https://arxiv.org/abs/2312.08273

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