Blar i forfatter "Debus, Sebastian"

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    • Combinatorics of Reflection Groups and Real Algebraic Geometry 

      Debus, Sebastian (Doctoral thesis; Doktorgradsavhandling, 2022-11-18)
      Real algebraic geometry studies sets defined by a finite system of real polynomial equalities and inequalities. A central topic in this area is the study of the cone of nonnegative polynomials. Verifying that a given polynomial is nonnegative is an NP-hard problem. However, it turns out to be algorithmically much more feasible to verify if a given polynomial admits a representation into a sum of ...

    • 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>. ...

    • Reflection groups and cones of sums of squares 

      Riener, Cordian; Debus, Sebastian (Journal article; Tidsskriftartikkel; Peer reviewed, 2023-03-15)
      We consider cones of real forms which are sums of squares and invariant under a (finite) reflection group. Using the representation theory of these groups we are able to use the symmetry inherent in these cones to give more efficient descriptions. We focus especially on the <i>A</i><sub>n</sub>, <i>B</i><sub>n</sub> and <i>D</i><sub>n</sub> case where we use so-called higher Specht polynomials to ...