3 problems

Strengthened 2-criticality conjecture. The set $\operatorname{gcs}(\alpha_{k,k'}L_s)$ is 2-critical and strong, and completes top down to $\alpha_{k,k'}L_s$.

Let $L(9)$ denote the Latin square of order $9$, and let $C$ be a critical set in $L(9)$. The minimum cardinality of a critical set in $L(9)$ is the $L(9)$ minimal critical-set con…

Let $L(2^n)$ be the Latin square of order $2^n$, with $n\geq 4$, and let $C$ be a critical set of minimal size in $L(2^n)$. Writing $S$ for this critical set, so that $|S|=|C|$, th…