3 problems

Let $P$ be a $0/1$ polytope, and let $G(P)$ be its graph, whose vertices are the vertices of $P$ and whose edges join pairs of vertices spanning an edge of $P$. Consider the simple…

The multiples-of-factorial conjecture. For any $n\in\mathbb{Z}_{>3}$, if $P,Q\subset\mathbb{R}^n$ are two arbitrary Ehrhart-equivalent integral $n$-polytopes, then

The factorial dilation conjecture. For any $n\in\mathbb{Z}_{\ge 1}$, if $P,Q\subset\mathbb{R}^n$ are arbitrary Ehrhart-equivalent integral $n$-polytopes, then they are…