3 problems

Let $T_1,T_2,\dots,T_k$ be a $K$-Knuth class of straight tableaux, and let $T_i$ have shape $\lambda_i$. Write … Order Young diagrams by inclusion, and let $[\lambda_i,\lambda_j]$…

Let $I_n$ denote the number of $K$-Knuth equivalence classes of initial tableaux on $[n]$, and let $U_n$ denote the number of unique rectification tableaux (URTs) on $[n]$. Asympto…

Let $T$ and $T'$ be tableaux with $T\equiv T'$. For a tableau $T$, let its size be the number of boxes in its shape, and let $w\overset{k}{\equiv}w'$ mean that $w$ and $w'$ can be…