4 problems

Let $P$ be a $d$-dimensional $0/1$-polytope, meaning the convex hull of a subset of the vertices of the $d$-cube. Facet-count conjecture. The polytope $P$ cannot have more than … f…

Let $g(n)$ be the maximum number of facets of a 0/1 polytope in $\mathbb{R}^n$. Facet-growth conjecture. The quantity $g(n)$ is of order $n^{n/2}$ as $n\to\infty$. The paper proves…

Let $P$ be a $d$-dimensional 0/1-polytope, meaning the convex hull of a set of points whose coordinates belong to $\{0,1\}$. Its graph has the vertices of $P$ as nodes and the edge…

A 0/1 $d$-polytope is a $d$-dimensional polytope whose vertices lie in $\{0,1\}^d$. Let edge expansion mean the minimum ratio of boundary edges to the size of a vertex subset of si…