论文标题
带有前缀的词典最不平方的单词
The lexicographically least square-free word with a given prefix
论文作者
论文摘要
具有给定前缀$ p $的非阴性整数字母上的词典最不平方的无限单词表示为$ l（p）$。当$ p $是一个空的单词时，瓜伊·帕奎特（Guay-Paquet）显示了这个单词，而Shallit则是标尺序列。对于其他前缀，该结构明显复杂得多。在本文中，我们表明$ l（p）$反映了几个单词$ p $的标尺序列的结构。我们提供的形态为字母$ n = 1 $和$ n \ geq3 $而产生$ l（n）$，以及大多数两个字母单词$ p $的家庭的$ l（p）$。
The lexicographically least square-free infinite word on the alphabet of non-negative integers with a given prefix $p$ is denoted $L(p)$. When $p$ is the empty word, this word was shown by Guay-Paquet and Shallit to be the ruler sequence. For other prefixes, the structure is significantly more complicated. In this paper, we show that $L(p)$ reflects the structure of the ruler sequence for several words $p$. We provide morphisms that generate $L(n)$ for letters $n=1$ and $n\geq3$, and $L(p)$ for most families of two-letter words $p$.
