论文标题
括号单词：由普遍多项式引起的斯特里亚语单词的概括
Bracket words: a generalisation of Sturmian words arising from generalised polynomials
论文作者
论文摘要
通用多项式是通过将地板函数，添加和乘法应用于多项式来构建的。尽管表面相似，但广义多项式表现出许多现象，对于多项式来说是不可能的。特别是，存在普遍的多项式序列，这些序列只有有限的许多值而不是周期性的。此类序列的示例包括Sturmian单词，以及更复杂的序列，例如$ [2 \ {πn^2 + \ sqrt {2} n [\ sqrt {3} n] \}] $。本文的目的是从单词上的Compinatorics的角度研究有限价值的广义多项式序列的字母到字母编码。我们从括号单词角度调查了广义多项式及其推论的现有结果，也证明了一些新的结果。我们的主要贡献是对括号单词的子单词复杂性的多项式结合。
Generalised polynomials are maps constructed by applying the floor function, addition, and multiplication to polynomials. Despite superficial similarity, generalised polynomials exhibit many phenomena which are impossible for polynomials. In particular, there exist generalised polynomial sequences which take only finitely many values without being periodic; examples of such sequences include the Sturmian words, as well as more complicated sequences like $[ 2\{ πn^2 + \sqrt{2}n[\sqrt{3}n] \}]$. The purpose of this paper is to investigate letter-to-letter codings of finitely-valued generalised polynomial sequences, which we call \emph{bracket words}, from the point of view of combinatorics on words. We survey existing results on generalised polynomials and their corollaries in terms of bracket words, and also prove several new results. Our main contribution is a polynomial bound on the subword complexity of bracket words.
