科研之友
微信
新浪微博
Facebook
分享链接
摘要
We study the lexicographically least infinite a/b-power-free word on the alphabet of non-negative integers. Frequently this word is a fixed point of a uniform morphism, or closely related to one. For example, the lexicographically least 7/4-power-free word is a fixed point of a 50847-uniform morphism. We identify the structure of the lexicographically least a/b-power-free word for three infinite families of rationals a/b as well many "sporadic" rationals that do not seem to belong to general families. To accomplish this, we develop an automated procedure for proving a/b-power-freeness for morphisms of a certain form, both for explicit and symbolic rational numbers a/b. 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 the finite alphabet {0, 1, 2}, and its sequence of letters is 353-automatic.
- 出版日期2018-5-25
