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arXiv · 2509.22619

Most frequent subsequences in a word

Boris Bukh·Aleksandre Saatashvili
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Abstract

We prove that every $n$-letter word over $k$-letter alphabet contains some word as a subsequence in at least $k^{n/4k(1+o(1))}$ many ways, and that this is sharp as $k\to\infty$. For fixed $k$, we show that the analogous number deviates from $μ_k^n$, for some constant $μ_k$, by a factor of at most $n$.

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Boris Bukh, Aleksandre Saatashvili. 2025-09-26. Most frequent subsequences in a word. https://arxiv.org/abs/2509.22619

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