9 problems

Baranwal–Shallit's conjecture. No other binary rich sequence has a smaller critical exponent than $2+\frac{\sqrt{2}}{2}$. This conjecture concerns the minimum possible critical exp…

Rampersad–Shallit–Vandomme conjecture. For every alphabet size $d\geq 5$, the minimal critical exponent among balanced sequences over a $d$-letter alphabet equals

Let $\gamma=[01,2,02]$ and let ${\mathbf G}=\gamma^\omega(0)$ be its fixed point. Its factor complexity is $2n+1$, and its critical exponent is $\mu=2+\frac{1}{\lambda^2-1}$, where…

Let ${\bf G}$ be the infinite ternary word described in the source, with critical exponent $2.4808627\cdots$ and factor complexity $2n+1$ for every $n\geq 1$. Shur's conjecture. Th…

Let $k\geq 1$, and let $\mathbf{x}_k$ be the Thue-Morse-like sequence described in the source. The critical exponent is the supremum of the exponents of its finite factors, while t…

For each integer $k\geq 1$, let ${\bf x}_k$ be the infinite word defined as the limit of the locally catenative sequence described above. The critical exponent conjecture for…

New conjecture. For every alphabet size $d\geq 11$, the minimal critical exponent of a balanced sequence over a $d$-letter alphabet equals

Rampersad et al.'s conjecture. The smallest possible critical exponent of an infinite balanced word over a $5$-letter alphabet is

Critical-exponent conjecture. Every infinite binary word avoiding the pattern $xxx^R$ has critical exponent