The (bitwise) complement $\overline{x}$ of a binary word $x$ is obtained by changing each $0$ in $x$ to $1$ and vice versa. An $\textit{antisquare}$ is a nonempty word of the form $x\, \overline{x}$. In this paper, we study infinite binary words that do not contain arbitrarily large antisquares. For example, we show that the repetition threshold for the language of infinite binary words containing exactly two distinct antisquares is $(5+\sqrt{5})/2$. We also study repetition thresholds for related classes, where "two" in the previous sentence is replaced by a larger number. We say a binary word is $\textit{good}$ if the only antisquares it contains are $01$ and $10$. We characterize the minimal antisquares, that is, those words that are antisquares but all proper factors are good. We determine the growth rate of the number of good words of length $n$ and determine the repetition threshold between polynomial and exponential growth for the number of good words.

翻译：二进制单词$x$的（按位）补$\overline{x}$通过将$x$中的每个$0$改为$1$、每个$1$改为$0$得到。**反平方**是指形如$x\, \overline{x}$的非空单词。本文研究不包含任意大反平方的无限二进制单词。例如，我们证明恰好包含两个不同反平方的无限二进制单词语言的重复阈值为$(5+\sqrt{5})/2$。我们还研究了相关类别的重复阈值，其中前一句中的“两个”被替换为更大的数。如果一个二进制单词仅包含$01$和$10$作为反平方，则称其为**好的**。我们刻画了最小反平方，即那些本身是反平方但所有真因子均为好单词的单词。我们确定了长度为$n$的好单词数量的增长率，并给出了好单词数量从多项式增长到指数增长的重复阈值。