3 citations · 11 across the 13 of their papers we have counts for
6 papers · 1 filter
On lattice coverings by locally anti-blocking bodies and polytopes with few vertices
Matthias Schymura, Jun Wang, Fei Xue
In 2021, Ordentlich, Regev and Weiss made a breakthrough that the lattice covering density of any -dimensional convex body is upper bounded by , improving on the best pr…
Deep lattice points in zonotopes, lonely runners, and lonely rabbits
Matthias Beck, Matthias Schymura
Let be a convex body and let be an interior point of . The coefficient of asymmetry $\operatorname{ca}(K,\mathb…
Packing minima and lattice points in convex bodies
Martin Henk, Matthias Schymura, Fei Xue
Motivated by long-standing conjectures on the discretization of classical inequalities in the Geometry of Numbers, we investigate a new set of parameters, which we call \emph{packi…
Tropical Ehrhart Theory and Tropical Volume
Georg Loho, Matthias Schymura
We introduce a novel intrinsic volume concept in tropical geometry. This is achieved by developing the foundations of a tropical analog of lattice point counting in polytopes. We e…
On the reverse isodiametric problem and Dvoretzky-Rogers-type volume bounds
Bernardo González Merino, Matthias Schymura
The isodiametric inequality states that the Euclidean ball maximizes the volume among all convex bodies of a given diameter. We are motivated by a conjecture of Makai Jr.~on the re…
On densities of lattice arrangements intersecting every i-dimensional affine subspace
Bernardo González Merino, Matthias Henze
In 1978, Makai Jr. established a remarkable connection between the volume-product of a convex body, its maximal lattice packing density and the minimal density of a lattice arrange…