We study the lexicographically least infinite $a/b$-power-free word on thealphabet of non-negative integers. Frequently this word is a fixed point of auniform morphism, or closely related to one. For example, the lexicographicallyleast $7/4$-power-free word is a fixed point of a $50847$-uniform morphism. Weidentify the structure of the lexicographically least $a/b$-power-free word forthree infinite families of rationals $a/b$ as well many "sporadic" rationalsthat do not seem to belong to general families. Along the way, we develop anautomated procedure for proving $a/b$-power-freeness for morphisms of a certainform. Finally, we establish a connection to words on a finite alphabet. Namely,the lexicographically least $27/23$-power-free word is in fact a word on thefinite alphabet ${0, 1, 2}$, and its sequence of letters is $353$-automatic.
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机译：我们在非负整数的Thalphabet上研究了词典上最少无限的免费A / B $ -Power-PORD。经常这个词是一个肛门般的态势的一个固定点，或者与一个密切相关。例如，词典上积分$ 7/4 $ -power-a -power-tod是一个50847美元$-inform态态的固定点。 Weidentify尾词的结构最少$ a / b $ -power-flug word verthree无限族的理性家庭$ a / b $和许多“零星的”理性似乎没有属于普通家庭。一路上，我们开发了证明$ A / B $ -Power -Power-Freeness的Asutomated程序。最后，我们建立了一个有限字母表上的文字的连接。即，词典上最少27/23点$ -Power的单词实际上是小型字母$ {0,1,2 } $的单词，它的字母序列是353美元 - 自动。
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