关于极大无界因子
On Maximal Unbordered Factors
摘要：
给定一个长度为$n$的字符串$S$，它的最大无边界因子是没有边界的最长因子。本文研究了$n$与$S$的最大无边因子的长度之间的关系。我们证明了对于大小为$σ\ge 5$的字母表，长度为~ $n$的字符串的最大无边界因子的期望长度至少为$0.99 n$（对于$n$的足够大的值）。作为该结果的应用，我们提出了一种计算字符串最大无边界因子的新算法。
英文摘要：
Given a string $S$ of length $n$, its maximal unbordered factor is the longest factor which does not have a border. In this work we investigate the relationship between $n$ and the length of the maximal unbordered factor of $S$. We prove that for the alphabet of size $σ\ge 5$ the expected length of the maximal unbordered factor of a string of length~$n$ is at least $0.99 n$ (for sufficiently large values of $n$). As an application of this result, we propose a new algorithm for computing the maximal unbordered factor of a string.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
