Antisquares and Critical Exponents

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