34 citations · 90 across the 14 of their papers we have counts for
18 papers
Diagonal Specht ideals and their varieties
Anna Escofet, Cordian Riener, Hugues Verdure
We study the diagonal Specht ideals , , generated by the -isoty…
Homotopy type of shellable -complexes and their homology groups
Sudhir R. Ghorpade, Rakhi Pratihar, Tovohery H. Randrianarisoa +2
The theory of shellable simplicial complexes brings together combinatorics, algebra, and topology in a remarkable way. Initially introduced by Alder for -simplicial complexes, r…
Symmetric SAGE and SONC forms, exactness and quantitative gaps
Philippe Moustrou, Cordian Riener, Thorsten Theobald +1
The classes of sums of arithmetic-geometric exponentials (SAGE) and of sums of nonnegative circuit polynomials (SONC) provide nonnegativity certificates which are based on the ineq…
Symmetries in polynomial optimization
Philippe Moustrou, Cordian Riener, Hugues Verdure
This chapter investigates how symmetries can be used to reduce the computational complexity in polynomial optimization problems. A focus will be specifically given on the Moment-SO…
The poset of Specht ideals for hyperoctahedral groups
Sebastian Debus, Philippe Moustrou, Cordian Riener +1
Specht polynomials classically realize the irreducible representations of the symmetric group. The ideals defined by these polynomials provide a strong connection with the combinat…
Weight Spectra of Gabidulin Rank-metric Codes and Betti Numbers
Trygve Johnsen, Rakhi Pratihar, Hugues Verdure
We consider -matroids and their associated classical matroids derived from Gabidulin rank-metric codes. We express the generalized rank weights of a Gabidulin rank-metric code i…
Symmetry reduction in AM/GM-based optimization
Philippe Moustrou, Helen Naumann, Cordian Riener +2
The arithmetic mean/geometric mean-inequality (AM/GM-inequality) facilitates classes of non-negativity certificates and of relaxation techniques for polynomials and, more generally…
Greedy weights for matroids
Trygve Johnsen, Hugues Verdure
We introduce greedy weights of matroids, inspired by those for linear codes. We show that a Wei duality holds for two of these types of greedy weights for matroids. Moreover we sho…
Symmetric ideals, Specht polynomials and solutions to symmetric systems of equations
Philippe Moustrou, Cordian Riener, Hugues Verdure
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 poly…
Higher weight spectra of Veronese codes
Trygve Johnsen, Hugues Verdure
We study q-ary linear codes C obtained from Veronese surfaces over finite fields. We show how one can find the higher weight spectra of these codes, or equivalently, the weight dis…
Flags of almost affine codes
Trygve Johnsen, Hugues Verdure
We describe a two-party wire-tap channel of type II in the framework of almost affine codes. Its cryptological performance is related to some relative profiles of a pair of almost…
Generalized Hamming weights for almost affine codes
Trygve Johnsen, Hugues Verdure
We define generalized Hamming weights for almost affine codes. We show how various aspects and applications of generalized Hamming weights for linear codes, such as Wei duality, ge…
A generalization of Kung's theorem
Trygve Johnsen, Keisuke Shiromoto, Hugues Verdure
We give a generalization of Kung's theorem on critical exponents of linear codes over a finite field, in terms of sums of extended weight polynomials of linear codes. For all i=k+1…
Betti numbers of skeletons
Jan Roksvold, Hugues Verdure
We demonstrate that the Betti numbers associated to an N-graded minimal free resolution of the Stanley-Reisner ring of the (d-1)-skeleton of a simplicial complex of dimension d can…
A generalization of weight polynomials to matroids
Trygve Johnsen, Jan Roksvold, Hugues Verdure
Generalizing polynomials previously studied in the context of linear codes, we define weight polynomials and an enumerator for a matroid . Our main result is that these polynomi…
Betti numbers associated to the facet ideal of a matroid
Trygve Johnsen, Jan Nyquist Roksvold, Hugues Verdure
To a matroid M with n edges, we associate the so-called facet ideal F(M) generated by monomials corresponding to bases of M. We show that the Betti numbers related to an N-graded m…
Stanley-Reisner resolution of constant weight linear codes
Trygve Johnsen, Hugues Verdure
Given a constant weight linear code, we investigate its weight hierarchy and the Stanley-Reisner resolution of its associated matroid regarded as a simplicial complex. We also exhi…
Hamming weights and Betti numbers of Stanley-Reisner rings associated to matroids
Trygve Johnsen, Hugues Verdure
To each linear code over a finite field we associate the matroid of its parity check matrix. We show to what extent one can determine the generalized Hamming weights of the code (o…