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arXiv · 2210.00342

Finding binary words with a given number of subsequences

Radosław Żak
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Abstract

We relate binary words with a given number of subsequences to continued fractions of rational numbers with a given denominator. We deduce that there are binary strings of length $O(\log n \log \log n)$ with exactly $n$ subsequences; this can be improved to $O(\log n)$ under assumption of Zaremba's conjecture.

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Radosław Żak. 2022-10-01. Finding binary words with a given number of subsequences. https://doi.org/10.1016/j.tcs.2022.03.032

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