Deciding positivity of multisymmetric polynomials

Deciding positivity of real polynomials

We describe an algorithm for deciding whether or not a real polynomial is positive semideenite. The question is reduced to deciding whether or not a certain zero-dimensional system of polynomial equations has a real root.

When is the Algebra of Multisymmetric Polynomials Generated by the Elementary Multisymmetric Polynomials?

Multisymmetric polynomials are the r-fold diagonal invariants of the symmetric group Sn. 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 polynomials with coefficients in A to be generated by the elementary multisymm...

Positivity Of Trigonometri Polynomials

Deciding Positivity of Littlewood-Richardson Coefficients

Starting with Knutson and Tao’s hive model [KT99], we characterize the Littlewood– Richardson coefficient c λ,μ of given partitions λ, μ, ν ∈ N as the number of capacity achieving hive flows on the honeycomb graph. Based on this, we design a polynomial time algorithm for deciding c λ,μ > 0. This algorithm is easy to state and takes O (

Positivity of Legendrian Thom polynomials

We study Legendrian singularities arising in complex contact geometry. We define a one-parameter family of bases in the ring of Legendrian characteristic classes such that any Legendrian Thom polynomial has nonnegative coefficients when expanded in these bases. The method uses a suitable Lagrange Grassmann bundle on the product of projective spaces. This is an extension of a nonnegativity resul...