Counting k-ary words by number of adjacency differences of a prescribed size

Sela Fried, Toufik Mansour, Mark Shattuck

Recently, the general problem of enumerating permutations $\pi ={\pi }_1\cdots {\pi }_n$ such that ${\pi }_{i+r}-{\pi }_i\ne s$ for all $1\le i\le n-r$, where $r$ and $s$ are fixed, was considered by…