论文标题
在非负整数的字母上避免5/4能力
Avoiding 5/4-powers on the alphabet of nonnegative integers
论文作者
论文摘要
我们确定了词典上最少的单词的结构，避免了非负整数字母上的5/4能力。具体而言，我们表明该单词具有$pτ（φ（z）φ^2（z）\ cdots）$的形式，其中$ p，z $是有限的单词，$φ$是6-均匀的形态，$τ$是编码。此描述产生了$ i $ th字母的复发，我们用来证明字母的顺序为6个常规，等级为188。更一般而言，我们证明$ k $ regularity是满足相同类型复发的序列的$ k $ regularity。
We identify the structure of the lexicographically least word avoiding 5/4-powers on the alphabet of nonnegative integers. Specifically, we show that this word has the form $p τ(φ(z) φ^2(z) \cdots)$ where $p, z$ are finite words, $φ$ is a 6-uniform morphism, and $τ$ is a coding. This description yields a recurrence for the $i$th letter, which we use to prove that the sequence of letters is 6-regular with rank 188. More generally, we prove $k$-regularity for a sequence satisfying a recurrence of the same type.
