Ten Squares Force an Overlap

Fuente: arXiv
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Main Author: Shallit, Jeffrey
Format: Preprint
Published: 2026
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author Shallit, Jeffrey
author_facet Shallit, Jeffrey
contents We prove that every concatenation of $10$ or more binary squares contains an overlap. The bound $10$ is best possible. In contrast, over a ternary alphabet, there are infinitely long overlap-free words that consist of a concatenation of squares.
format Preprint
id arxiv_https___arxiv_org_abs_2605_28570
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Ten Squares Force an Overlap
Shallit, Jeffrey
Combinatorics
Discrete Mathematics
Formal Languages and Automata Theory
We prove that every concatenation of $10$ or more binary squares contains an overlap. The bound $10$ is best possible. In contrast, over a ternary alphabet, there are infinitely long overlap-free words that consist of a concatenation of squares.
title Ten Squares Force an Overlap
topic Combinatorics
Discrete Mathematics
Formal Languages and Automata Theory
url https://arxiv.org/abs/2605.28570