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Winfried Bruns

  1. Hilbert depth of powers of the maximal ideal.

    Втр, 02/09/2010 - 16:01 — SomNambul
    Authors: Winfried Bruns, Christian Krattenthaler, Jan Uliczka
    Subjects: Commutative Algebra
    Abstract

    The Hilbert depth of a module M is the maximum depth that occurs among all
    modules with the same Hilbert function as M. In this note we compute the
    Hilbert depths of the powers of the irrelevant maximal ideal in a standard
    graded polynomial ring.

  2. Challenging computations of Hilbert bases of cones associated with algebraic statistics.

    Втр, 01/26/2010 - 16:01 — SomNambul
    Authors: Winfried Bruns, Bogdan Ichim, Raymond Hemmecke, Matthias Koeppe, Christof Soeger
    Subjects: Combinatorics
    Abstract

    In this paper we present two independent computational proofs that the monoid
    derived from $5\times 5\times 3$ contingency tables is normal, completing the
    classification by Hibi and Ohsugi. We show that Vlach's vector disproving
    normality for the monoid derived from $6\times 4\times 3$ contingency tables is
    the unique minimal such vector up to symmetry. Finally, we compute the full
    Hilbert basis of the cone associated with the non-normal monoid of the
    semi-graphoid for $|N|=5$. The computations are based on extensions of the
    packages LattE-4ti2 and Normaliz.

  3. Normaliz: Algorithms for Affine Monoids and Rational Cones.

    Пт, 10/16/2009 - 17:25 — SomNambul
    Authors: Winfried Bruns, Bogdan Ichim
    Subjects: Commutative Algebra
    Abstract

    Normaliz is a program for solving linear systems of inequalities. In this
    paper we present the algorithms implemented in the program, starting with
    version 2.0.

  4. Stanley decompositions and Hilbert depth in the Koszul complex.

    Пт, 09/04/2009 - 12:10 — SomNambul
    Authors: Winfried Bruns, Christian Krattenthaler, Jan Uliczka
    Subjects: Commutative Algebra
    Abstract

    Stanley decompositions of multigraded modules $M$ over polynomials rings have
    been discussed intensively in recent years. There is a natural notion of depth
    that goes with a Stanley decomposition, called the Stanley depth. Stanley
    conjectured that the Stanley depth of a module $M$ is always at least the
    (classical) depth of $M$. In this paper we introduce a weaker type of
    decomposition, which we call Hilbert decomposition, since it only depends on
    the Hilbert function of $M$, and an analogous notion of depth, called Hilbert
    depth.

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