计算林登子序列
Counting Lyndon Subsequences
摘要：
计算保留某些属性的子串/序列（例如，回文，平方）是弦学中一个重要的数学兴趣。最近，Glen等人研究了弦中林登因子的个数。如果一个字符串$w = uv$在其所有共轭$vu$中是字典中最小的，则称之为林登字。在本文中，我们考虑一个更一般的问题“计数林登连续性”。我们给出了（1）一个字符串中Lyndon连续性的最大总数，（2）一个字符串中Lyndon连续性的期望总数，（3）一个字符串中不同Lyndon连续性的期望数目.
英文摘要：
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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