Prefix normal words are binary words with the property that no factor has more 1s than the prefix of the same length. Finite prefix normal words were introduced in Fici and Lipták (2011) [18]. In this paper, we study infinite prefix normal words and explore their relationship to some known classes of infinite binary words. In particular, we establish a connection between prefix normal words and Sturmian words, between prefix normal words and abelian complexity, and between prefix normality and lexicographic order.¹

中文翻译：

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在无限前缀普通词上

前缀普通字是具有不超过相同长度前缀的1的属性的二进制字。有限前缀普通词在Fici和Lipták（2011）中引入[18]。在本文中，我们研究了无限前缀普通词，并探讨了它们与某些已知类别的无限二进制词的关系。特别是，我们在前缀普通词与Sturmian词之间，前缀普通词与阿贝尔复杂性之间以及前缀正态性与词典顺序之间建立了联系。^1个