CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt155",{id:"formSmash:upper:j_idt155",widgetVar:"widget_formSmash_upper_j_idt155",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt159_j_idt161",{id:"formSmash:upper:j_idt159:j_idt161",widgetVar:"widget_formSmash_upper_j_idt159_j_idt161",target:"formSmash:upper:j_idt159:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Non-representable hyperbolic matroidsPrimeFaces.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});
function selectAll()
{
var panelSome = $(PrimeFaces.escapeClientId("formSmash:some"));
var panelAll = $(PrimeFaces.escapeClientId("formSmash:all"));
panelAll.toggle();
toggleList(panelSome.get(0).childNodes, panelAll);
toggleList(panelAll.get(0).childNodes, panelAll);
}
/*Toggling the list of authorPanel nodes according to the toggling of the closeable second panel */
function toggleList(childList, panel)
{
var panelWasOpen = (panel.get(0).style.display == 'none');
// console.log('panel was open ' + panelWasOpen);
for (var c = 0; c < childList.length; c++) {
if (childList[c].classList.contains('authorPanel')) {
clickNode(panelWasOpen, childList[c]);
}
}
}
/*nodes have styleClass ui-corner-top if they are expanded and ui-corner-all if they are collapsed */
function clickNode(collapse, child)
{
if (collapse && child.classList.contains('ui-corner-top')) {
// console.log('collapse');
child.click();
}
if (!collapse && child.classList.contains('ui-corner-all')) {
// console.log('expand');
child.click();
}
}
2018 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 334, p. 417-449Article in journal (Refereed) Published
##### Abstract [en]

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

Academic Press, 2018. Vol. 334, p. 417-449
##### Keywords [en]

Hyperbolic polynomial, Generalized Lax conjecture, Matroid, Hyperbolic matroid
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-233273DOI: 10.1016/j.aim.2018.03.038ISI: 000440392700009Scopus ID: 2-s2.0-85049357702OAI: oai:DiVA.org:kth-233273DiVA, id: diva2:1239622
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt523",{id:"formSmash:j_idt523",widgetVar:"widget_formSmash_j_idt523",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt529",{id:"formSmash:j_idt529",widgetVar:"widget_formSmash_j_idt529",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt535",{id:"formSmash:j_idt535",widgetVar:"widget_formSmash_j_idt535",multiple:true});
##### Funder

Swedish Research CouncilKnut and Alice Wallenberg Foundation
##### Note

##### In thesis

The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. Hyperbolic polynomials give rise to a class of (hyperbolic) matroids which properly contains the class of matroids representable over the complex numbers. This connection was used by the second author to construct counterexamples to algebraic (stronger) versions of the generalized Lax conjecture by considering a non-representable hyperbolic matroid. The Vamos matroid and a generalization of it are, prior to this work, the only known instances of non-representable hyperbolic matroids. We prove that the Non-Pappus and Non-Desargues matroids are non-representable hyperbolic matroids by exploiting a connection between Euclidean Jordan algebras and projective geometries. We further identify a large class of hyperbolic matroids which contains the Vamos matroid and the generalized Vamos matroids recently studied by Burton, Vinzant and Youm. This proves a conjecture of Burton et al. We also prove that many of the matroids considered here are non representable. The proof of hyperbolicity for the matroids in the class depends on proving nonnegativity of certain symmetric polynomials. In particular we generalize and strengthen several inequalities in the literature, such as the Laguerre Turan inequality and an inequality due to Jensen. Finally we explore consequences to algebraic versions of the generalized Lax conjecture.

QC 20180817

Available from: 2018-08-17 Created: 2018-08-17 Last updated: 2019-05-10Bibliographically approved1. Combinatorics and zeros of multivariate polynomials$(function(){PrimeFaces.cw("OverlayPanel","overlay1314811",{id:"formSmash:j_idt841:0:j_idt848",widgetVar:"overlay1314811",target:"formSmash:j_idt841:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
urn-nbn$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_j_idt1519",{id:"formSmash:j_idt1519",widgetVar:"widget_formSmash_j_idt1519",showEffect:"fade",hideEffect:"fade",showDelay:500,hideDelay:300,target:"formSmash:altmetricDiv"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1573",{id:"formSmash:lower:j_idt1573",widgetVar:"widget_formSmash_lower_j_idt1573",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1574_j_idt1578",{id:"formSmash:lower:j_idt1574:j_idt1578",widgetVar:"widget_formSmash_lower_j_idt1574_j_idt1578",target:"formSmash:lower:j_idt1574:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});