2 problems

Odd-shift inclusion conjecture. If $k$ is odd, then $X_1\subset X_2$.

Let $a$ and $b$ be positive integers with $2a<b$, and let $u$ be a partition that is both $\operatorname{Reg}{a,b}$-valid and $\operatorname{Colreg}{a,b}$-valid. For each hook…