An isoperimetric inequality for word overlap

TL;DR

This paper establishes an asymptotically sharp upper bound on the product of densities for two sets of words with no suffix-prefix overlaps, extending isoperimetric inequalities to word combinatorics.

Contribution

It introduces a novel isoperimetric inequality for word sets with no suffix-prefix overlaps, providing a tight asymptotic bound.

Findings

Product of densities bounded by (1+o(1))/(en)

Bound is asymptotically sharp

Applicable to finite alphabet word sets

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.