2 problems

For $n\geq1$ and $0\leq k<n/2$, let … The notation $[\varnothing,\lambda]_{\mathrm{shift}}$ denotes the corresponding initial interval in the shifted Young's lattice,…

Let $\delta_r=(r,r-1,\ldots,1)$, and for partitions let $\nu+\lambda$ denote the partition obtained by adding corresponding parts. For $a,m,n\geq 1$ with $n>am$, set … Here…