Discriminants, symmetrized graph monomials, and sums of squares

Details Discriminants, symmetrized graph monomials, and sums of squares Discriminants, symmetrized graph monomials, and sums of squares

2011-04-04

arxiv.org/abs/1104.0589v1

Mathematics

Algebraic Geometry

Scientific paper

Motivated by the necessities of the invariant theory of binary forms J. J. Sylvester constructed in 1878 for each graph with possible multiple edges but without loops its symmetrized graph monomial which is a polynomial in the vertex labels of the original graph. In the 20-th century this construction was studied by several authors. We pose the question for which graphs this polynomial is a non-negative resp. a sum of squares. This problem is motivated by a recent conjecture of F. Sottile and E. Mukhin on discriminant of the derivative of a univariate polynomial, and an interesting example of P. and A. Lax of a graph with 4 edges whose symmetrized graph monomial is non-negative but not a sum of squares. We present detailed information about symmetrized graph monomials for graphs with four and six edges, obtained by computer calculations.

Affiliated with

Also associated with

No associations

Rating

Discriminants, symmetrized graph monomials, and sums of squares does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Discriminants, symmetrized graph monomials, and sums of squares, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Discriminants, symmetrized graph monomials, and sums of squares will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-318100