On the context-freeness of the set of words containing overlaps

The analogue of overlap-freeness for the period-doubling sequence

Good words are binary words avoiding factors 11 and 1001, and patterns 0000 and 00010100. We show that good words bear the same relationship to the period-doubling sequence that overlap-free words bear to the Thue-Morse sequence. We prove an analogue of Fife's Theorem for good words, exhibit the lexicographically least and greatest infinite good words, and determine the patterns avoided by the period doubling word.

Fibonacci态射的overlap-freeness类似物

The analogue of overlap-freeness for the Fibonacci morphism

本文定义了不含$4^-$-幂和因子11的faux-bonacci词，证明其与Fibonacci态射的关系等同于overlap-free词与Thue-Morse态射的关系，并给出了Fife定理的类似物及字典序极值无穷词的刻画。

Binary words containing infinitely many overlaps

We characterize the squares occurring in infinite overlap-free binary words and construct various alpha power-free binary words containing infinitely many 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。

$H$-自由边删除问题的NP-难度

NP-Hardness of the $H$-Free Edge-Deletion Problem

本文证明对任意含圈的图$H$，$H$-自由边删除问题为NP-难，从而证实猜想并完整刻画该问题的计算复杂性。

关于保持出现的映射

On Occurrence-Preserving Morphisms

本文研究了保持出现的映射，引入了无干扰映射的概念，并通过该概念对保持出现的映射进行了精确刻画，应用于Fibonacci和Thue-Morse词以识别其最小唯一子字符串，并简化了现有关于净出现的证明。