Zobrazeno 1 - 10
of 52
pro vyhledávání: '"Moustrou, Philippe"'
Let $G$ be a finite group acting linearly on $\mathbb{R}^n$. A celebrated Theorem of Procesi and Schwarz gives an explicit description of the orbit space $\mathbb{R}^n /\!/G$ as a basic closed semi-algebraic set. We give a new proof of this statement
Externí odkaz:
http://arxiv.org/abs/2407.08339
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
Trigonometric polynomials are usually defined on the lattice of integers.We consider the larger class of weight and root lattices with crystallographic symmetry.This article gives a new approach to minimize trigonometric polynomials, which are invari
Externí odkaz:
http://arxiv.org/abs/2303.09487
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
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
Publikováno v:
In Journal of Symbolic Computation March-April 2025 127
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. We apply this to get sharp bounds for packing problems, and we use
Externí odkaz:
http://arxiv.org/abs/2001.00256
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
Publikováno v:
J. London Math. Soc. (2) 104 (2021) 1135-1171
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
Externí odkaz:
http://arxiv.org/abs/1907.09751