6 problems

For integers $k\geq 2$ and $\ell\geq 1$, let $R(k,\ell)$ be the generalized repetition threshold: the critical exponent separating finite from infinite words over a $k$-letter alph…

Let $\mathcal{C}_d$ be the class of $d$-ary sequences rich in palindromes. For each $n\in\mathbb{N}$, let $\mathbf{u}_n$ denote the sequence defined in the paper by the correspondi…

Let $\mathcal{C}_d$ be the class of $d$-ary sequences rich in palindromes, and let … be the repetition threshold, where $E(\mathbf{u})$ is the critical exponent of a sequence. Curr…

A word is called $r$-free if it contains no factor of exponent at least $r$. Let $\operatorname{RT}(n)$ be the infimum of the real numbers $r$ for which there exist arbitrarily lon…

For each integer $k\geq 4$, let $\mathrm{RT}(k)$ be the repetition threshold, and let $\mathrm{CRT}_{\mathrm{W}}(k)$ and $\mathrm{CRT}_{\mathrm{I}}(k)$ be respectively the infima o…

For a circular word, define the strong circular repetition threshold by … Here a circular word is $\beta$-free if it has no factor of exponent at least $\beta$. Gorbunova's conject…