Ten Squares Force an Overlap
Combinatorics
2026-05-28 v1 Discrete Mathematics
Formal Languages and Automata Theory
Abstract
We prove that every concatenation of or more binary squares contains an overlap. The bound is best possible. In contrast, over a ternary alphabet, there are infinitely long overlap-free words that consist of a concatenation of squares.
Cite
@article{arxiv.2605.28570,
title = {Ten Squares Force an Overlap},
author = {Jeffrey Shallit},
journal= {arXiv preprint arXiv:2605.28570},
year = {2026}
}