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Spectrahedrality of hyperbolicity cones of multivariate matching polynomialsPrimeFaces.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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2018 (English)In: Journal of Algebraic Combinatorics, ISSN 0925-9899, E-ISSN 1572-9192Article in journal (Refereed) In press
##### Abstract [en]

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

Springer, 2018.
##### Keywords [en]

matching polynomial, independence polynomial, generalized Lax conjecture, spectrahedral representation
##### National Category

Discrete Mathematics
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-250763OAI: oai:DiVA.org:kth-250763DiVA, id: diva2:1313629
#####

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##### Note

##### In thesis

The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. We prove the conjecture for a multivariate generalization of the matching polynomial. This is further extended (albeit in a weaker sense) to a multivariate version of the independence polynomial for simplicial graphs. As an application we give a new proof of the conjecture for elementary symmetric polynomials (originally due to Brändén). Finally we consider a hyperbolic convolution of determinant polynomials generalizing an identity of Godsil and Gutman.

QC 20190510

Available from: 2019-05-05 Created: 2019-05-05 Last updated: 2020-04-14Bibliographically 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});});

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