4 papers
On Diamond-Free Subgroup Lattices
Matt Alexander
In this paper we introduce a particular lattice of subgroups called a "cyclic-diamond" and show that every finite non-cyclic group contains a cyclic-diamond as a sublattice of its…
Geometry and volume product of finite dimensional Lipschitz-free spaces
Matthew Alexander, Matthieu Fradelizi, Luis C. García-Lirola +1
The goal of this paper is to study geometric and extremal properties of the convex body , which is the unit ball of the Lipschitz-free Banach space associated wi…
Polytopes of Maximal Volume Product
Matthew Alexander, Matthieu Fradelizi, Artem Zvavitch
For a convex body , let $K^z = \{y\in{\mathbb R}^n : \langle y-z, x-z\rangle\le 1, \mbox{\ for all\ } x\in K\}$ be the polar body of with respect to th…
A discrete version of Koldobsky's slicing inequality
Matthew Alexander, Martin Henk, Artem Zvavitch
Let be a number of integer lattice points contained in a set . In this paper we prove that for each there exists a constant depending on onl…