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Alexandersson, PerShapiro, Boris
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Discriminants, Symmetrized Graph monomials and Sums of SquaresPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2012 (English)In: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 21, no 4, p. 353-361Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2012. Vol. 21, no 4, p. 353-361
##### Keywords [en]

polynomial sums of squares, translation-invariant polynomials, graph monomials, sums of squares, discriminants, symmetric polynomials
##### National Category

Mathematics
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:su:diva-84745DOI: 10.1080/10586458.2012.669608ISI: 000313614400003OAI: oai:DiVA.org:su-84745DiVA, id: diva2:581344
#####

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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt757",{id:"formSmash:j_idt757",widgetVar:"widget_formSmash_j_idt757",multiple:true}); Available from: 2012-12-31 Created: 2012-12-31 Last updated: 2022-02-24Bibliographically approved
##### In thesis

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.

1. Combinatorial Methods in Complex Analysis$(function(){PrimeFaces.cw("OverlayPanel","overlay613664",{id:"formSmash:j_idt1297:0:j_idt1306",widgetVar:"overlay613664",target:"formSmash:j_idt1297:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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