论文标题
加权前缀普通词：注意差距
Weighted Prefix Normal Words: Mind the Gap
论文作者
论文摘要
前缀正常单词是一个二进制词，其前缀至少包含1S的任何一个相同长度的因素。 FICI和Lipták在2011年引入的前缀正态性的概念到目前为止仅针对二元字母上的单词定义。在这项工作中，我们研究了有限单词对任意有限字母的概括，即加权前缀正态性。我们证明加权前缀正态性比二进制前缀正态性更具表现力。此外，我们研究了加权前缀正常形式的存在，因为加权前缀正态性带有几种在二进制案例中尚未发生的新特点。我们表征了这些问题，并最终提出了一种标准技术，以获得所有过于有限的，有限的字母的通用前缀正常形式。
A prefix normal word is a binary word whose prefixes contain at least as many 1s as any of its factors of the same length. Introduced by Fici and Lipták in 2011 the notion of prefix normality is so far only defined for words over the binary alphabet. In this work we investigate a generalisation for finite words over arbitrary finite alphabets, namely weighted prefix normality. We prove that weighted prefix normality is more expressive than binary prefix normality. Furthermore, we investigate the existence of a weighted prefix normal form since weighted prefix normality comes with several new peculiarities that did not already occur in the binary case. We characterise these issues and finally present a standard technique to obtain a generalised prefix normal form for all words overarbitrary, finite alphabets.
