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
AI总结：
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。
摘要：
我们确定了互补对称Rote序列的临界指数和回归函数。这些公式以与相应标准Sturmian序列的S-adic表示相关的连分数展开式来表达。结果基于对Sturmian序列的双特殊因子的回归词的深入研究。利用临界指数的公式，我们描述了所有临界指数小于或等于3的互补对称Rote序列，并证明了存在不可数多个互补对称Rote序列，其临界指数小于Fibonacci序列的临界指数。我们的研究受到Baranwal和Shallit提出的关于富含回文序列的猜想的启发。该猜想最近由Curie、Mol和Rampersad解决，他们使用了两个特定的互补对称Rote序列。
英文摘要：
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.
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