4 problems

Partition characterization. Every minimal halfspace with respect to ${\mathcal P}$ has the form

Let $X$ be a closed TC-convex set, and for each $a\in\mathbb T_{\pm}^{d+1}$ let $\overline{\mathcal{H}}^+(a)$ denote the corresponding closed tropical halfspace. Halfspace represen…

Develin–Yu's conjecture. A tropical cone is pure and full-dimensional if and only if it has a half-space description in which the apices of these tropical half-spaces are in genera…

Let ${\mathcal B}^d=[0,1]^d$ be the $d$-dimensional box equipped with max-T convexity, and let $X$ be a set of $(d+1)(r-1)+1$ points in ${\mathcal B}^d$. Tverberg's theorem for max…