Blar i forfatter "Moustrou, Philippe"

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    • Coloring the Voronoi tessellation of lattices 

      Dutour Sikirić, Mathieu; Madore, David A.; Moustrou, Philippe; Vallentin, Frank (Journal article; Tidsskriftartikkel; Peer reviewed, 2021-05-03)
      In this paper we define the chromatic number of a lattice: It is the least number of colors one needs to color the interiors of the cells of the Voronoi tessellation of a lattice so that no two cells sharing a facet are of the same color. We compute the chromatic number of the root lattices, their duals, and of the Leech lattice, we consider the chromatic number of lattices of Voronoi’s first ...

    • Exact semidefinite programming bounds for packing problems 

      Dostert, Maria; de Laat, David; Moustrou, Philippe (Journal article; Tidsskriftartikkel; Peer reviewed, 2021-05-25)
      In this paper we give an algorithm to round the floating point output of a semidefinite programming solver to a solution over the rationals or a quadratic extension of the rationals. This algorithm does not require the solution to be strictly feasible and works for large problems. We apply this to get sharp bounds for packing problems, and we use these sharp bounds to prove that certain optimal ...

    • The poset of Specht ideals for hyperoctahedral groups 

      Debus, Sebastian; Moustrou, Philippe; Riener, Cordian Benedikt; Verdure, Hugues (Journal article; Tidsskriftartikkel, 2023)
      Specht polynomials classically realize the irreducible representations of the symmetric group. The ideals defined by these polynomials provide a strong connection with the combinatorics of Young tableaux and have been intensively studied by several authors. We initiate similar investigations for the ideals defined by the Specht polynomials associated to the hyperoctahedral group <i>B<sub>n</sub></i>. ...

    • Symmetric ideals, Specht polynomials and solutions to symmetric systems of equations 

      Moustrou, Philippe; Riener, Cordian; Verdure, Hugues (Journal article; Tidsskriftartikkel; Peer reviewed, 2021-02-18)
      An ideal of polynomials is symmetric if it is closed under permutations of variables. We relate general symmetric ideals to the so called Specht ideals generated by all Specht polynomials of a given shape. We show a connection between the leading monomials of polynomials in the ideal and the Specht polynomials contained in the ideal. This provides applications in several contexts. Most notably, this ...

    • Symmetry Reduction in AM/GM-Based Optimization 

      Verdure, Hugues; Moustrou, Philippe; Naumann, Helen; Riener, Cordian; Theobald, Thorsten (Journal article; Tidsskriftartikkel; Peer reviewed, 2022)
      The arithmetic mean/geometric mean inequality (AM/GM inequality) facilitates classes of nonnegativity certificates and of relaxation techniques for polynomials and, more generally, for exponential sums. Here, we present a first systematic study of the AM/GM-based techniques in the presence of symmetries under the linear action of a finite group. We prove a symmetry-adapted representation theorem and ...