Location of Repository

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

Topics:
Mathematics - Algebraic Geometry

Year: 2011

DOI identifier: 10.1080/10586458.2012.669608

OAI identifier:
oai:arXiv.org:1104.0589

Provided by:
arXiv.org e-Print Archive

Download PDF:To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.