7 problems

Let $T$ be a standard tableau, and call $T$ good when every permutation $w$ satisfying $\operatorname{Q}(w)=T$ is BBS good, equivalently when $T$ is the recording tableau of some g…

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 a box-ball system have $n$ blocks, with $Q_k$ balls in the $k$-th block, and suppose the blocks are separated sufficiently so that the asymptotic soliton structure can be ident…

Let $\Phi(n,k)$ have initial configuration $(\mathbf{Y}_i^0)_i$ consisting only of positive solitons. Interchange space and time so that $\mathbf{Y}_i^t$ and $\mathbf{Z}_i^t$ are r…

Finite-carrier conjecture. When only positive solitons occur in $\Phi(n,k)$, the carriers $\mathbf{Z}_i^t$ take values in the finite set $M$. This is intended to express the observ…

Let $X\in\mathbb{R}^{M\times N}$ and let $\mathrm{UD}(\eta)$ denote the ultradiscretization of the mapping $\eta$ constructed from the divisor component and the ultradiscretized ma…

The loops around the cylinder are called whurls, and a whurl relation is the transformation $R$ on the parameters of adjacent whurls that preserves boundary measurements. In the mi…