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arXiv · 2106.01190

Counting Lyndon Subsequences

Ryo Hirakawa·Yuto Nakashima·Shunsuke Inenaga·Masayuki Takeda
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Abstract

Counting substrings/subsequences that preserve some property (e.g., palindromes, squares) is an important mathematical interest in stringology. Recently, Glen et al. studied the number of Lyndon factors in a string. A string $w = uv$ is called a Lyndon word if it is the lexicographically smallest among all of its conjugates $vu$. In this paper, we consider a more general problem "counting Lyndon subsequences". We show (1) the maximum total number of Lyndon subsequences in a string, (2) the expected total number of Lyndon subsequences in a string, (3) the expected number of distinct Lyndon subsequences in a string.

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Ryo Hirakawa, Yuto Nakashima, Shunsuke Inenaga, Masayuki Takeda. 2021-06-02. Counting Lyndon Subsequences. https://arxiv.org/abs/2106.01190

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