论文标题
一个单词时期数量的不平等
An inequality for the number of periods in a word
论文作者
论文摘要
我们证明，根据X的长度及其初始关键指数，单词X中的时期数量是不平等的。接下来，我们表征了特征性斯特里式单词的长度-n前缀的所有时期，从n的懒惰ostrowski表示，并使用此结果表明我们的不平等对于无限多个单词x来说是紧密的。我们提出了两个相关的无限单词周期性措施。最后，我们还考虑了X无重叠或无方形的特殊情况。
We prove an inequality for the number of periods in a word x in terms of the length of x and its initial critical exponent. Next, we characterize all periods of the length-n prefix of a characteristic Sturmian word in terms of the lazy Ostrowski representation of n, and use this result to show that our inequality is tight for infinitely many words x. We propose two related measures of periodicity for infinite words. Finally, we also consider special cases where x is overlap-free or squarefree.
