Discriminants, Symmetrized Graph monomials and Sums of Squares
2012 (English)In: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 21, no 4, 353-361 p.Article in journal (Refereed) Published
In 1878, motivated by the requirements of the invariant the-ory of binary forms, J. J. Sylvester constructed, for every graphwith possible multiple edges but without loops, its symmetrizedgraph monomial, which is a polynomial in the vertex labels ofthe original graph. We pose the question for which graphs thispolynomial is nonnegative or a sum of squares. This problem ismotivated by a recent conjecture of F. Sottile and E. Mukhin onthe discriminant of the derivative of a univariate polynomial andby an interesting example of P. and A. Lax of a graph with fouredges whose symmetrized graph monomial is nonnegative butnot a sum of squares. We present detailed information about sym-metrized graph monomials for graphs with four and six edges,obtained by computer calculations.
Place, publisher, year, edition, pages
2012. Vol. 21, no 4, 353-361 p.
polynomial sums of squares, translation-invariant polynomials, graph monomials, sums of squares, discriminants, symmetric polynomials
Research subject Mathematics
IdentifiersURN: urn:nbn:se:su:diva-84745DOI: 10.1080/10586458.2012.669608ISI: 000313614400003OAI: oai:DiVA.org:su-84745DiVA: diva2:581344