2 problems

Let $\lambda=(\lambda_1,\lambda_2)\vdash n$ with $\ell(\lambda)=2$, and set $l_\lambda=\max\{\lambda_1,\lambda_2+1\}$. For $l_\lambda\le m\le n$, let $\mathsf{Par}(\lambda;m)$ be t…

Let $\lambda$ be a partition with $\ell(\lambda)\le 2$, and let $\mathcal{E}_{\lambda;m}$, $\mathsf{Par}(\lambda;m)$, $\mathbf{G}_E$, and $X_\mu$ be the sets and $0$-Hecke modules…