一个词中句号个数的不等式
An inequality for the number of periods in a word
摘要：
我们证明了一个不等式的周期数在一个字x的长度x和它的初始临界指数。接下来，我们刻画了一个特征Sturmian词的长度为n的前缀的所有周期的懒惰的Ostrowski表示的n，并使用这个结果表明，我们的不等式是紧无限多个字x。我们提出了两个相关的措施的周期性无限的话。最后，我们还考虑了x是无平方或无平方的特殊情况。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
