再谈关于C^∞—字幂的一个猜想

DISCUSSION ON A CONJECTURE FOR THE POWERS OF C ∞ WORDS

设Ｗ是一个Ｃ∞－字，且｜Ｗ｜＞３，若对一切满足｜Ｄｋ（Ｗ）｜＞１的自然数ｋ，都有Ｄｋ（Ｗ）的首末两个循环中至少有一个循环的长为２，则称Ｗ是一个弱偶Ｃ∞－字．本文讨论了弱偶Ｃ∞－字的性质，证明了以下的结论：若Ｗ是一个弱偶Ｃ∞－字。

Let W be a C ∞ word with |W|>3. The C ∞ word W is called a weakly even C ∞ word if at least one of the first run or last run of D r(W) has length two, for any natural number r with |D r(W)|>1. In this paper we have proved following result: If W is a weakly even C ∞ word, then W 2 is not C ∞ word.