All Questions

Given a polyhedron $$Ax\geq b$$ is there an $NC^1$ or an $NC^2$ algorithm to count the number of vertices $\bmod2$? Assume $A\in\{0,1\}^{m\times n}$ and $b\in\mathbb Z^{m}$ ($m=O(n)$) and assume rows ...

Let $P$ be a convex lattice polytope in $\mathbb{R}^n$. The function $L(t, P) = |\mathbb{Z}^n \cap t\cdot P|$ is a polynomial, and we have an equality $$L(-t, P) = (-1)^nL(t, P^{int}),$$ where $P^{int}...