Concept
Théorème fondamental des fonctions symétriques
Publications associées (44)
K3 surfaces, cyclotomic polynomials and orthogonal groups
Let X be a complex projective K3 surface and let T-X be its transcendental lattice; the characteristic polynomials of isometries of T-X induced by automorphisms of X are powers of cyclotomic polynomials. Which powers of cyclotomic polynomials occur? The ai ...
Springer Int Publ Ag2024A Determinantal Identity for the Permanent of a Rank 2 Matrix
We prove an identity relating the permanent of a rank 2 matrix and the determinants of its Hadamard powers. When viewed in the right way, the resulting formula looks strikingly similar to an identity of Carlitz and Levine, suggesting the possibility that t ...
TAYLOR & FRANCIS INC2022Optimal radial basis for density-based atomic representations
Michele Ceriotti, Sergey Pozdnyakov, Jigyasa Nigam, Félix Benedito Clément Musil, Alexander Jan Goscinski
The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular representations ...
AIP Publishing2021Variants of Homomorphism Polynomials Complete for Algebraic Complexity Classes
We present polynomial families complete for the well-studied algebraic complexity classes VF, VBP, VP, and VNP. The polynomial families are based on the homomorphism polynomials studied in the recent works of Durand et al. (2014) and Mahajan et al. (2018). ...
ASSOC COMPUTING MACHINERY2021Interacting with Explanations through Critiquing
Boi Faltings, Claudiu-Cristian Musat, Diego Matteo Antognini
Using personalized explanations to support recommendations has been shown to increase trust and perceived quality. However, to actually obtain better recommendations, there needs to be a means for users to modify the recommendation criteria by interacting ...
2021On arithmetic progressions in symmetric sets in finite field model
We consider two problems regarding arithmetic progressions in symmetric sets in the finite field (product space) model. First, we show that a symmetric set S subset of Z(q)(n) containing vertical bar S vertical bar = mu . q(n) elements must contain at leas ...
ELECTRONIC JOURNAL OF COMBINATORICS2020Polynomial Evaluation on Superscalar Architecture, Applied to the Elementary Function e(x)
Felix Schürmann, Francesco Cremonesi, Timothée Ewart
The evaluation of small degree polynomials is critical for the computation of elementary functions. It has been extensively studied and is well documented. In this article, we evaluate existing methods for polynomial evaluation on superscalar architecture. ...
2020