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Local formulas for Ehrhart coefficients from lattice tiles
As shown by McMullen in 1983, the coefficients of the Ehrhart polynomial of a lattice polytope can be written as a weighted sum of facial volumes. The weights in such a local formula depend only on the outer n...

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Open AccessA simplex algorithm for rational cpfactorization
In this paper we provide an algorithm, similar to the simplex algorithm, which determines a rational cpfactorization of a given matrix, whenever the matrix allows such a factorization. This algorithm can be u...

Article
On the topological computation of \(K_4\) of the Gaussian and Eisenstein integers
In this paper we use topological tools to investigate the structure of the algebraic Kgroups \(K_4(R)\) ...

Article
The impact of dependence among voters’ preferences with partial indifference
365体育网站 Standard weighted scoring rules do not directly accommodate the possibility that some voters might have dichotomous preferences in threecandidate elections. The direct solution to this issue would be to requi...

Article
On LatticeFree Orbit Polytopes
Given a permutation group acting on coordinates of \({{\mathbb {R}}}^n\) ...

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Exploiting polyhedral symmetries in social choice
365体育网站 A large amount of literature in social choice theory deals with quantifying the probability of certain election outcomes. One way of computing the probability of a specific voting situation under the Impartial...

Chapter
Exploiting Symmetries in Polyhedral Computations
In this note we give a short overview on symmetry exploiting techniques in three different branches of polyhedral computations: The representation conversion problem, integer linear programming and lattice poi...

Article
Open AccessThe Contact Polytope of the Leech Lattice
The contact polytope of a lattice is the convex hull of its shortest vectors. In this paper we classify the facets of the contact polytope of the Leech lattice up to symmetry. There are 1,197,362,269,604,214,2...

Chapter and Conference Paper
C++ Tools for Exploiting Polyhedral Symmetries
We report on the recently developed C++ tools PermLib and SymPol that are designed to support high performance work with symmetric polyhedra. The callable library PermLib provides basic support for permutation gr...

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Instability of discrete point sets]{Instability of discrete point sets
365体育网站 Let <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ...

Article
Lattices of Optimal Finite Lattice Packings
We consider finite lattice ball packings with respect to parametric density and show that densest packings are attained in critical lattices if the number of translates and the density parameter are sufficient...

Article
The spherical conjecture in Minkowski geometry
We show that the shapes of convex bodies containing m translates of a convex body K, so that their Minkowskian surface area is minimum, tends for growing m to a convex body L.

Chapter
A Discrete Isoperimetric Inequality and Its Application to Sphere Packings
We consider finite packings of equal spheres in Euclidean 3–space E^{3}. The convex hull of the sphere centers is the packing polytope. In the first part of the paper we prove a tight inequality between the surface ...

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A criterion for finite lattice coverings
For a centrally symmetric convex \(K \subset E^2 \) and a covering lattice L for K, a lattice polygon P is called a...

Article
Polyhedral Models of Felix Klein’s Group