Lattice-Width Directions and Minkowski's $3^d$-Theorem Page 1 Copyright © by SIAM.
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1. Introduction. The first ideas of convex sets date as far back as Archimedes but it was not
until the end of the last century that a systematic study gave rise to the subject as an …

We study upper bounds on the number of lattice points for convex bodies having their
centroid at the origin. For the family of simplices as well as in the planar case we obtain best …

Minkowski's second theorem on successive minima asserts that the volume of a 0-symmetric
convex body K over the covolume of a lattice Λ can be bounded above by a quantity …

Abstract A lattice (d, k)-polytope is the convex hull of a set of points in dimension d whose
coordinates are integers ranging between 0 and k. We consider the largest possible …

A note on bounds on the minimum area of convex lattice polygons Page 1 BULL. AUSTRAL.
MATH. SOC. 11HO6 VOL. 45 (1992) [237-240] A NOTE ON BOUNDS ON THE MINIMUM …

Let K be a convex body in n-dimensional Euclidean space R"(ni> 2), V (K)> 0 its n-
dimensional volume, A (K) its (n-1)-dimensional surface area, and L (K) the number of lattice …

In this paper we consider connections between three classes of optimal (in different senses)
convex lattice polygons. A classical result is that if G is a strictly convex curve of length s …

The main purpose of this note is to prove an upper bound on the number of lattice points of a
centrally symmetric convex body in terms of the successive minima of the body. This bound …

The main result of this paper is an inequality relating the lattice point enumerator of a 3-
dimensional, 0-symmetric convex body and its successive minima. This is an example of …