4 problems

Let $v_1^0,\dots,v_m^0$ be positive integers and set $\boldsymbol{v}_0=(v_1^0,\dots,v_m^0)$. The rational envelope of $\boldsymbol{v}_0$ is the ambient rational-affine object in wh…

Let $P\subset\mathbb{R}^n$ be a rational polytope with minimum Ehrhart quasi-period $N$. Two subsets of $\mathbb{R}^n$ are $\operatorname{GL}_n(\mathbb{Z})$-equidecomposable if the…

Let $P\subset\mathbb{R}^n$ be a rational polytope, and let its Ehrhart quasi-polynomial have quasi-period $1$. An open simplex is the relative interior of a simplex, and it is inte…

A rational polytope is a polytope whose vertices have rational coordinates. A subdivision decomposes a polytope into polyhedral pieces, and affine unimodular transformations are af…