关于平衡序列及其临界指数
On balanced sequences and their critical exponent
摘要：
研究了有限字母表上的非周期平衡序列。这种类型的序列vv完全由Sturmian序列u和两个恒定间隙序列y和y '表征。我们表明，V的语言最终是树枝状的，我们专注于返回的话，它的因素。给出了平衡序列的临界指数和渐近临界指数的一种计算方法，条件是相关的Sturmian序列u具有二次斜率。该方法是基于寻找最短的返回字的双特殊因素在v.我们说明我们的方法上的几个例子，特别是我们证实了一个猜想Rampersad，Shallit和Vandomme，两个特定的序列有最小的关键指数之间的所有平衡序列超过9个字母（分别，$0-字母）字母表。
英文摘要：
We study aperiodic balanced sequences over finite alphabets. A sequence vv of this type is fully characterised by a Sturmian sequence u and two constant gap sequences y and y'. We show that the language of v is eventually dendric and we focus on return words to its factors. We develop a method for computing the critical exponent and asymptotic critical exponent of balanced sequences, provided the associated Sturmian sequence u has a quadratic slope. The method is based on looking for the shortest return words to bispecial factors in v. We illustrate our method on several examples; in particular we confirm a conjecture of Rampersad, Shallit and Vandomme that two specific sequences have the least critical exponent among all balanced sequences over 9-letter (resp., $0-letter) alphabets.
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