2 problems

The type B piecewise-linear homomesy conjecture. The statistic $h^{\mathrm{PL}}_*\colon \mathcal{A}^{\mathrm{PL}}_{\kappa}(\mathsf{B}^n)\to \mathbb{R}$ is $\kappa$-mesic for…

Let $Y_m$ and $Z_m$ be solutions of ultradiscrete Painlevé VI without parity variables, with fixed parity variables $\frak{y}_m=\frak{z}_m=-1$ for all $m$, and let $Q,A_i,B_i$ be t…