Mathematics > Combinatorics
arXiv:2605.28570 (math)
[Submitted on 27 May 2026 (v1), last revised 15 Aug 2026 (this version, v2)]
Abstract: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.
Submission history
From: Jeffrey Shallit [view email]
[v1]
Wed, 27 May 2026 14:56:13 UTC (8 KB)
[v2]
Sat, 15 Aug 2026 20:15:27 UTC (8 KB)
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