We show that the number of lattice directions in which a d-dimensional convex body in R^d has minimum width is at most 3^d-1, with equality only for the regular cross-polytope.
Jan 10, 2009
We show that the number of lattice directions in which a convex body in $\mathbb{R}^d$ has minimum width is at most $3^d-1$, with equality only for the ...
Theorem I. Let P be a centrally-symmetric convex set in Rd with int(P) ∩ Zd = {0}. Then. |P ∩ Zd| ≤ 3d , where equality holds if and only if. P ∼= [−1,1]d.
We show that the number of lattice directions in which a convex body in ℝ d has minimum width is at most 3 d -1, with equality only for the regular ...
Jan 1, 2012 · LATTICE-WIDTH DIRECTIONS AND MINKOWSKI'S 3d-THEOREM. ∗. JAN DRAISMA†, TYRRELL B. MCALLISTER‡, AND BENJAMIN NILL§. Abstract. We show that the ...
We show that the number of lattice directions in which a convex body in $\mathbb{R}^d$ has minimum width is at most $3^d-1$, with equality only for the ...
Our approach is based on what is known as the Cayley trick for Minkowski sums. A direct consequence of our result is a tight asymptotic bound on the complexity ...
We show that the number of lattice directions in which a d-dimensional convex body in R^d has minimum width is at most 3^d-1, with equality only for the ...
Jan 10, 2009 · LATTICE WIDTH DIRECTIONS AND MINKOWSKI'S 3d-THEOREM. 3. Lemma 2.1. The lattice width of S relative to Zd is equal to that of π(S) relative to ...
Minkowski's theorem states that if the volume of S is strictly greater than 2n d(L), then S must contain at least one lattice point other than the origin. ( ...
Missing: Width Directions
People also ask
What is the Minkowski's uniqueness theorem?
What is the Cevian area theorem?