Zobrazeno 1 - 10
of 111
pro vyhledávání: '"Verdure, P."'
Autor:
Ghorpade, Sudhir R., Pratihar, Rakhi, Randrianarisoa, Tovohery H., Verdure, Hugues, Wilson, Glen
The theory of shellable simplicial complexes brings together combinatorics, algebra, and topology in a remarkable way. Initially introduced by Alder for $q$-simplicial complexes, recent work of Ghorpade, Pratihar, and Randrianarisoa extends the study
Externí odkaz:
http://arxiv.org/abs/2403.07102
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 inequality of the arithmetic and geometric means. We study the cones of sy
Externí odkaz:
http://arxiv.org/abs/2312.10500
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-SOS hierarchy in polynomial optimization, where results from representat
Externí odkaz:
http://arxiv.org/abs/2305.05219
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 a
Externí odkaz:
http://arxiv.org/abs/2206.08925
We consider $q$-matroids and their associated classical matroids derived from Gabidulin rank-metric codes. We express the generalized rank weights of a Gabidulin rank-metric code in terms of Betti numbers of the dual classical matroid associated to t
Externí odkaz:
http://arxiv.org/abs/2106.10993
The arithmetic mean/geometric mean-inequality (AM/GM-inequality) facilitates classes of non-negativity certificates and of relaxation techniques for polynomials and, more generally, for exponential sums. Here, we present a first systematic study of t
Externí odkaz:
http://arxiv.org/abs/2102.12913
Autor:
Johnsen, Trygve, Verdure, Hugues
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 show that in the cases where the matroids involved are associated to line
Externí odkaz:
http://arxiv.org/abs/2002.08824
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 mon
Externí odkaz:
http://arxiv.org/abs/1912.05266
Autor:
Johnsen, Trygve, Verdure, Hugues
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 distribution of all extension codes of C over all field extensions of the
Externí odkaz:
http://arxiv.org/abs/1904.07626
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