Relation between powers of factors and recurrence function characterizing Sturmian words

正则树上的拟Sturmian着色

Quasi-Sturmian colorings on regular trees

本文研究正则树上的拟Sturmian着色，将其分为有界与无界两类，提出类似Sturmian着色的归纳算法，并利用回归函数区分这两类着色。

Sturmian Jungle (or Garden?) on Multiliteral Alphabets

The properties characterizing Sturmian words are considered for words on multiliteral alphabets. We summarize various generalizations of Sturmian words to multiliteral alphabets and enlarge the list of known relationships among these generalizations. We also collect many examples of infinite words to illustrate differences in the generalized definitions of Sturmian words.

互补对称Rote序列：临界指数与回归函数

Complementary symmetric Rote sequences: the critical exponent and the recurrence function

本文确定了互补对称Rote序列的临界指数和回归函数，利用连分数展开和回归词分析，描述了临界指数≤3的序列，并证明存在不可数多个序列的临界指数小于Fibonacci序列，受Baranwal-Shallit猜想启发。

关于无限词中的模递归和窗口复杂度

On modulo-recurrence and window complexity in infinite words

引入均匀模递归和强模递归概念，证明Sturmian词和最大复杂度词是强模递归的，并建立Thue-Morse词窗口复杂度与经典复杂度的关系，构造窗口复杂度有界或呈次线性增长的词，证明一致递归非周期词的窗口复杂度无界。

Characterizing Alternating Sign Triangles

Alternating sign triangles were introduced by Carroll and Speyer in relation to cube recurrence, by analogy to alternating sign matrices for octahedron recurrence. Permutation triangles are the alternating sign triangles whose entries are either 0 or 1, by analogy with permutation matrices. In this paper, we prove a simple characterization of permutation triangles, originally conjectured by Glick. We will also prove some properties of alternating sign triangles.

因子平衡性、线性递归与因子复杂度

Factor-balancedness, linear recurrence, and factor complexity

本文研究了无限字的因子平衡性与线性递归关系，提出通用条件并构造了具有指数复杂度的因子平衡字示例。