M. C. Zimmermann

collaborators

3 papers

math.NT2025

Diameter and Girth of Representation Graphs of Quadratic Forms

Nico Lorenz, Marc Christian Zimmermann

Let $q$ be a non-degenerate quadratic form defined on an $F$ vector space $V$ and $a \in F$ . We consider the Cayley graph on $V$ with generating set ${x \in V ∣ q (x) = a}$ and…

math.MG2025

Polarization of lattices: Stable cold spots and spherical designs

Christine Bachoc, Philippe Moustrou, Frank Vallentin +1

We consider the problem of finding the minimum of inhomogeneous Gaussian lattice sums: Given a lattice $L \subseteq R^{n}$ and a positive constant $α$ , the goal is to find t…

math.CO2024

The chromatic number of 4-dimensional lattices

Frank Vallentin, Stephen Weißbach, Marc Christian Zimmermann

The chromatic number of a lattice in n-dimensional Euclidean space is defined as the chromatic number of its Voronoi graph. The Voronoi graph is the Cayley graph on the lattice hav…