4 problems

Rank characterization theorem. The Frobenius rank of $D$ coincides with the highest power of $t$ dividing

Self-conjugate skew-equivalence conjecture. If

Power-of-two conjecture. Every skew-equivalence class of skew diagrams has cardinality a power of $2$.

For $n\geq 1$, $k\geq 0$, and a partition $\lambda$ such that the skew diagrams $\mathcal{S}(\lambda,k,n)$ and $\mathcal{S}(\lambda^t,k,n)$ are connected, write…