论文标题
绝不正方形的三元单词的长度
Lengths of extremal square-free ternary words
论文作者
论文摘要
如果每个单词从$ w $获得的每个单词通过插入$σ$（在任何位置）中包含一个正方形的单个字母，则固定字母$σ$上的无方$ w $都是极端的。 Grytczuk等。最近介绍了无极大正方形词的概念，并证明存在任意长的无极端平方三元单词。我们发现所有允许极端无方形三元字的长度。特别是，我们表明每个足够大的长度都有一个无极端的三元字。我们还解决了圆形单词的类似问题。
A square-free word $w$ over a fixed alphabet $Σ$ is extremal if every word obtained from $w$ by inserting a single letter from $Σ$ (at any position) contains a square. Grytczuk et al. recently introduced the concept of extremal square-free word, and demonstrated that there are arbitrarily long extremal square-free ternary words. We find all lengths which admit an extremal square-free ternary word. In particular, we show that there is an extremal square-free ternary word of every sufficiently large length. We also solve the analogous problem for circular words.
