An isoperimetric inequality for word overlap

Abstract

Let $A$ and $B$ be sets of words of length $n$ over some finite alphabet. Suppose that no suffix of a word in $A$ coincides with a prefix of a word in $B$. Then we show that the product of densities of $A$ and $B$ is upper bounded by $(1+o(1))/(en)$. This bound is asymptotically sharp.

6 pages, updated with an asymptotically sharp bound; see end of introduction for additional credit