On subwords in the base-$q$ expansion of polynomial and exponential functions

Hajime Kaneko, Thomas Stoll

Let $w$ be any word over the alphabet $\{0,1,\dots ,q-1\}$, and denote by $h$ either a polynomial of degree $d\ge 1$ or $h:n\mapsto m^n$ for a fixed $m$. Furthermore, denote by…