3 problems

Let $k\geq 3$, and let $\{r_1,\dots,r_k\}$ be a set of distinct positive reals with $r_1>\dots>r_k>0$. A sequence over a $k$-element set is balanced if, for every symbol, the numbe…

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

Let $\mathcal{B}=\\{s\in\\{\mathtt{0},\mathtt{1}\\}^{\mathbb{Z}}:s\text{ is balanced}\\}$ be the set of all balanced bi-infinite binary sequences, and let … be their language of fi…