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arXiv · 2602.20143

An isoperimetric inequality for word overlap

Dmitrii Zakharov
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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.

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Dmitrii Zakharov. 2026-03-03. An isoperimetric inequality for word overlap. https://arxiv.org/abs/2602.20143

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