论文标题
关于有限词的广场数
On the number of squares in a finite word
论文作者
论文摘要
{\ em square}是$ uu $的单词。在本文中，我们证明，对于给定的有限单词$ w $，$ w $的不同平方因子的数量由$ | w | - | - | - | \ alphabet（w）|+1 $，其中$ | w | $表示$ w $ and $ w $ and $ | \ alphabet（w）的长度表示$ w $的不同字母的数量。该结果回答了1998年弗朗克尔（Fraenkel）和辛普森（Simpson）的猜想。
A {\em square} is a word of the form $uu$. In this paper we prove that for a given finite word $w$, the number of distinct square factors of $w$ is bounded by $|w|-|\Alphabet(w)|+1$, where $|w|$ denotes the length of $w$ and $|\Alphabet(w)|$ denotes the number of distinct letters in $w$. This result answers a conjecture of Fraenkel and Simpson stated in 1998.
