论文标题
在三元字母上的圆形单词的平衡和亚伯属性上
On balanced and abelian properties of circular words over a ternary alphabet
论文作者
论文摘要
我们重新审视平衡循环单词的分类问题，并专注于三元字母的情况。我们提出了基督徒单词离散近似表示的$ 3 $维概括。通过考虑在三元字母上平衡圆形单词的Abelian复杂性的最低限制的$ 3 $，我们在三元字母上提供了所有圆形单词的分类，其具有ABELIAN复杂性，但要遵守该界限。该结果还使我们能够构建一套无限的双限性词，其Abelian复杂性等于$ 3 $。
We revisit the question of classification of balanced circular words and focus on the case of a ternary alphabet. We propose a $3$-dimensional generalisation of the discrete approximation representation of Christoffel words. By considering the minimal bound $3$ for abelian complexity of balanced circular words over a ternary alphabet, we provide a classification of all circular words over a ternary alphabet with abelian complexity subject to this bound. This result also allows us to construct an uncountable set of bi-infinite aperiodic words with abelian complexity equal to $3$.
