论文标题
互补对称的死记硬背序列：关键指数和复发函数
Complementary symmetric Rote sequences: the critical exponent and the recurrence function
论文作者
论文摘要
我们确定互补对称死记硬背序列的临界指数和复发功能。该公式是根据与相应标准Sturmian序列的S-ADIC表示相关的持续分数扩展表示的。结果基于对斯特里派序列双重因素的回报词的彻底研究。使用临界指数的公式，我们描述了所有互补对称的死记硬背序列，其临界指数小于或等于3，我们表明，与纤维核序列的关键指数相比，有许多互补的对称的死记硬背序列小于临界指数。我们的研究是出于猜想的激励，对富含Baranwal和Shallit提出的palindromes的序列。 Curie，Mol和Rampersad的最新解决方案使用了两个特定的互补对称死记硬背序列。
We determine the critical exponent and the recurrence function of complementary symmetric Rote sequences. The formulae are expressed in terms of the continued fraction expansions associated with the S-adic representations of the corresponding standard Sturmian sequences. The results are based on a thorough study of return words to bispecial factors of Sturmian sequences. Using the formula for the critical exponent, we describe all complementary symmetric Rote sequences with the critical exponent less than or equal to 3, and we show that there are uncountably many complementary symmetric Rote sequences with the critical exponent less than the critical exponent of the Fibonacci sequence. Our study is motivated by a~conjecture on sequences rich in palindromes formulated by Baranwal and Shallit. Its recent solution by Curie, Mol, and Rampersad uses two particular complementary symmetric Rote sequences.
