2 citations · 3 across the 7 of their papers we have counts for
8 papers
Diameter and Girth of Representation Graphs of Quadratic Forms
Nico Lorenz, Marc Christian Zimmermann
Let be a non-degenerate quadratic form defined on an vector space and . We consider the Cayley graph on with generating set and…
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 and a positive constant , the goal is to find t…
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…
Cliques in Representation Graphs of Quadratic Forms
Nico Lorenz, Marc Christian Zimmermann
We study cliques in graphs arising from quadratic forms where the vertices are the elements of the module of the quadratic form and two vertices are adjacent if their difference re…
Bounds on polarization problems on compact sets via mixed integer programming
Jan Rolfes, Robert Schüler, Marc Christian Zimmermann
Finding point configurations, that yield the maximum polarization (Chebyshev constant) is gaining interest in the field of geometric optimization. In the present article, we study…
A semidefinite program for least distortion embeddings of flat tori into Hilbert spaces
Arne Heimendahl, Moritz Lücke, Frank Vallentin +1
We derive and analyze an infinite-dimensional semidefinite program which computes least distortion embeddings of flat tori , where is an -dimensional lattice…
Critical even unimodular lattices in the Gaussian core model
Arne Heimendahl, Aurelio Marafioti, Antonia Thiemeyer +2
We consider even unimodular lattices which are critical for potential energy with respect to Gaussian potential functions in the manifold of lattices having point density 1. All ev…
Steinitz classes and partial genera of unimodular lattices over imaginary-quadratic fields
Michael Jürgens, Marc C. Zimmermann
In this paper we first of all determine all possible genera of (odd and even) definite unimodular lattices over an imaginary-quadratic field. The main questions are whether the par…