2 problems

Let $H\subseteq\mathbb{R}^n$ be a finite set. Its Carathéodory rank $\operatorname{cr}(H)$ is the least integer $t$ such that every element of the integer cone generated by $H$ is…

Let $\mathfrak{S}$ be the set of points of a peg-solitaire board. Let $V(\mathfrak{S},\mathbb{Z})$ be the integer span of legal-move vectors and let $V^+(\mathfrak{S},\mathbb{Q})$…