Smooth words and Chebyshev polynomials

Arnold Knopfmacher, Toufik Mansour, Augustine Munagi +1

A word $\sigma ={\sigma }_1...{\sigma }_n$ over the alphabet $[k]=\{1,2,...,k\}$ is said to be {\em smooth} if there are no two adjacent letters with difference greater than 1. A word $\sigma$ is said to be…