Avoidance of split overlaps

卷曲数变换中的重复避免

Repetition Avoidance in Curling-Number Transforms

该研究针对字及其卷曲数变换的重复避免问题，通过Thue-Morse形态构造与穷举搜索得出：4是允许同时实现无限无重叠性的最小字母表大小，相关结果经Walnut验证。

Subword complexity and power avoidance

We begin a systematic study of the relations between subword complexity of infinite words and their power avoidance. Among other things, we show that -- the Thue-Morse word has the minimum possible subword complexity over all overlap-free binary words and all $(\frac 73)$-power-free binary words, but not over all $(\frac 73)^+$-power-free binary words; -- the twisted Thue-Morse word has the maximum possible subword complexity over all overlap-free binary words, but no word has the maximum subword complexity over all $(\frac 73)$-power-free binary words; -- if some word attains the minimum poss…