7 problems

Fix $z\in[0,1]$. Let $(u_0,v_0)=(\operatorname{RSK\ cos}z,\operatorname{RSK\ sin}z)$ be the corresponding point on the Logan--Shepp--Vershik--Kerov limit curve $\Omega_*$. For i.i.…

For a level $\ell$ and multipartition data $\mu,\nu$, let $\mathrm{ParMat}_{\nu,\mu}^{\flat}$ denote the corresponding set of enriched block matrices, let…

Let $\lambda$ be a partition with $n$ parts, and let $M=(m_{i,j})_{1\le i,j \le n}\in\mathcal{M}_\lambda$ be a minimal matrix of shape $\lambda$. A matrix is Hankel when its entrie…

For permutations $v,w\in S_n$, let $\operatorname{Q}(v)$ and $\operatorname{Q}(w)$ denote their recording tableaux under the Robinson–Schensted correspondence. The steady-state tim…

Let $cmathfrak{M}$ be the set of multisegments, let $cLambda(cmathfrak{m})$ be the RSK-standard representation attached to $cmathfrak{m}cincmathfrak{M}$, and let $cmathcal{R}'$ be…

Let $cmathfrak{m}$ be a multisegment with RSK data … For each ladder $cmathfrak{l}_i$, let $Z(cmathfrak{l}_i)$ be its irreducible representation, and define representations recursi…

Let $\mathcal{M}$ be the set of multisegments. For a multisegment $cmathfrak{m}$, let $cLambda(cmathfrak{m})$ be its RSK-standard representation, let $Z(cmathfrak{m})$ be the corre…