3 problems

Let $u$ be a forbidden sequence, and let $s(n,u)$ be the sequence produced by the algorithm referenced in the source. Linear growth conjecture. The length of $s(n,u)$ grows at most…

Let $u$ be a forbidden sequence and let $\operatorname{Sat}(n,u)$ denote the saturation function for sequences over an $n$-letter alphabet. A sequence is $u$-saturated if it is $r$…

Let $u$ be a sequence, and let $\operatorname{Sat}(u,n)$ denote its saturation function on an alphabet of size $n$. The saturation dichotomy. For every sequence $u$, either … or ……