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    Article

    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...

    Maren H. Ring, Achill Schürmann in Beiträge zur Algebra und Geometrie / Contr… (2020)

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    A simplex algorithm for rational cp-factorization

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

    Mathieu Dutour Sikirić, Achill Schürmann, Frank Vallentin in Mathematical Programming (2020)

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    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 K-groups \(K_4(R)\) ...

    Mathieu Dutour Sikirić, Herbert Gangl in Journal of Homotopy and Related Structures (2019)

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    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 three-candidate elections. The direct solution to this issue would be to requi...

    Erik Friese, William V. Gehrlein, Dominique Lepelley in Quality & Quantity (2017)

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    Article

    On Lattice-Free Orbit Polytopes

    Given a permutation group acting on coordinates of \({{\mathbb {R}}}^n\) ...

    Katrin Herr, Thomas Rehn, Achill Schürmann in Discrete & Computational Geometry (2015)

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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...

    Achill Schürmann in Social Choice and Welfare (2013)

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    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...

    Achill Schürmann in Discrete Geometry and Optimization (2013)

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    Open Access

    The 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...

    Mathieu Dutour Sikirić, Achill Schürmann in Discrete & Computational Geometry (2010)

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    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...

    Thomas Rehn, Achill Schürmann in Mathematical Software – ICMS 2010 (2010)

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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 ...

    Achill Schürmann in Periodica Mathematica Hungarica (2006)

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    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...

    Ulrich Betke, Achill Schürmann in Monatshefte für Mathematik (2005)

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    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.

    Achill Schürmann in Archiv der Mathematik (2004)

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    Chapter

    A Discrete Isoperimetric Inequality and Its Application to Sphere Packings

    We consider finite packings of equal spheres in Euclidean 3–space E3. 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 ...

    Peter Scholl, Achill Schürmann, Jörg M. Wills in Discrete and Computational Geometry (2003)

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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...

    Uwe Schnell, Achill Schürmann in Periodica Mathematica Hungarica (2002)

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    Article

    Polyhedral Models of Felix Klein’s Group

    Peter Scholl, Achill Schürmann, J. M. Wills in The Mathematical Intelligencer (2002)