论文标题
阿贝尔封闭无限二进制单词
Abelian Closures of Infinite Binary Words
论文作者
论文摘要
如果每个字母在$ u $和$ v $中同样多次出现，则两个有限的单词$ u $和$ v $称为Abelian同等数字。 Abelian闭合$ \ Mathcal {a}（\ Mathbf {x}）$（偏移孔的闭合）无限单词$ \ Mathbf {X} $是无限单词$ \ Mathbf {y} $的集合$ \ mathbf {x} $，相当于$ u $。阿贝尔闭合的概念给出了斯特里亚语单词的特征：在二进制统一的经常性单词中，sturmian单词正是$ \ nathcal {a}（\ mathbf {x}）$等于shift orbit Orbit litter litture $ω（\ shiphbf {x}）$。在本文中，我们表明，与较大的字母相反，Abelian闭合均匀地复发的上二元二进制单词，而不是Sturmian，它包含无限的最低次要乘坐。
Two finite words $u$ and $v$ are called Abelian equivalent if each letter occurs equally many times in both $u$ and $v$. The abelian closure $\mathcal{A}(\mathbf{x})$ of (the shift orbit closure of) an infinite word $\mathbf{x}$ is the set of infinite words $\mathbf{y}$ such that, for each factor $u$ of $\mathbf{y}$, there exists a factor $v$ of $\mathbf{x}$ which is abelian equivalent to $u$. The notion of an abelian closure gives a characterization of Sturmian words: among binary uniformly recurrent words, Sturmian words are exactly those words for which $\mathcal{A}(\mathbf{x})$ equals the shift orbit closure $Ω(\mathbf{x})$. In this paper we show that, contrary to larger alphabets, the abelian closure of a uniformly recurrent aperiodic binary word which is not Sturmian contains infinitely many minimal subshifts.
