34 citations · 90 across the 14 of their papers we have counts for
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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…
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…
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…
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…
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…