Moscow Journal of Combinatorics and Number Theory
- Mosc. J. Comb. Number Theory
- Volume 8, Number 4 (2019), 367-378.
Discrete analogues of John's theorem
As a discrete counterpart to the classical theorem of Fritz John on the approximation of symmetric -dimensional convex bodies by ellipsoids, Tao and Vu introduced so called generalized arithmetic progressions in order to cover (many of) the lattice points inside a convex body by a simple geometric structure. Among others, they proved that there exists a generalized arithmetic progressions such that . Here we show that this bound can be lowered to and study some general properties of so called unimodular generalized arithmetic progressions.
Mosc. J. Comb. Number Theory, Volume 8, Number 4 (2019), 367-378.
Received: 14 April 2019
Revised: 27 May 2019
Accepted: 16 June 2019
First available in Project Euclid: 29 October 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11H06: Lattices and convex bodies [See also 11P21, 52C05, 52C07] 52C07: Lattices and convex bodies in $n$ dimensions [See also 11H06, 11H31, 11P21]
Secondary: 52A40: Inequalities and extremum problems
Berg, Sören Lennart; Henk, Martin. Discrete analogues of John's theorem. Mosc. J. Comb. Number Theory 8 (2019), no. 4, 367--378. doi:10.2140/moscow.2019.8.367. https://projecteuclid.org/euclid.moscow/1572314453