3 problems

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