BRIAND , Emmanuel

Couples of proper, non-empty real projective conics can be classified modulo rigid isotopy and ambient isotopy. We characterize the classes by equations, inequations and inequalities in the coefficients of the quadratic forms defining the conics. The results are well–adapted to the study of the relative position of two conics defined by...

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Multisymmetric polynomials are the $r$-fold diagonal invariants of the symmetric group ${\mathfrak{S}}_n$. Elementary multisymmetric polynomials are analogues of the elementary symmetric polynomials, in the multisymmetric setting. In this paper, we give a necessary and sufficient condition on a ring $A$ for the algebra of multisymmetric...

We give three proofs of the following result conjectured by Carriegos, De Castro-Garc\'ıa and Muñoz Castañeda in their work on enumeration of control systems: when (k+12)≤n<(k+22), there are as many partitions of n with k corners as pairs of partitions (α,β) such that (k+12)+|α|+|β|=n.

A matrix function, depending on a parameter t, and interpolating between the determinant and the permanent, is introduced. It is shown this function admits a simple expansion in terms of determinants and permanents of sub-matrices. This expansion is used to explain some formulas occurring in the resolution of some systems of algebraic equations.

We give three proofs of the following result conjectured by Carriegos, De Castro-García and Muñoz Castañeda in their work on enumeration of control systems: when ( k+1 2 ) ≤ n < ( k+2 2 ) , there are as many partitions of n with k corners as pairs of partitions (α, β) such that ( k+1 2 ) + |α| + |β| = n.