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arXiv · 2512.12077

Asymptotically half of binary words are shuffle squares

Xiaoyu He·Logan Post
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Abstract

A binary shuffle square is a binary word of even length that can be partitioned into two disjoint, identical subwords. Huang, Nam, Thaper, and the first author conjectured that as $n\rightarrow \infty$, asymptotically half of all binary words of length $2n$ are shuffle squares. We prove this conjecture in a strong form, by showing that the number of binary shuffle squares of length $2n$ is $(\frac{1}{2} - o(n^{-1/15})) 2^{2n}$.

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Xiaoyu He, Logan Post. 2025-12-12. Asymptotically half of binary words are shuffle squares. https://arxiv.org/abs/2512.12077

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