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Stable multivariate generalizations of 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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(English)Manuscript (preprint) (Other academic)
##### Abstract [en]

##### Keywords [en]

generalized matching polynomial, stable polynomial, hypergraph
##### National Category

Discrete Mathematics
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-250765OAI: oai:DiVA.org:kth-250765DiVA, id: diva2:1313632
#####

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##### Note

##### In thesis

The first part of this note concerns stable averages of multivariate matching polynomials. In proving the existence of infinite families of bipartite Ramanujan d-coverings, Hall, Puder and Sawin introduced the d-matching polynomial of a graph G, defined as the uniform average of matching polynomials over the set of d-sheeted covering graphs of G. We prove that a natural multivariate version of the d-matching polynomial is stable, consequently giving a short direct proof of the real-rootedness of the d-matching polynomial. Our theorem also includes graphs with loops, thus answering a question of said authors. Furthermore we define a weaker notion of matchings for hypergraphs and prove that a family of natural polynomials associated to such matchings are stable. In particular this provides a hypergraphic generalization of the classical Heilmann-Lieb theorem.

QC 20190510

Available from: 2019-05-05 Created: 2019-05-05 Last updated: 2019-05-13Bibliographically approved1. Combinatorics and zeros of multivariate polynomials$(function(){PrimeFaces.cw("OverlayPanel","overlay1314811",{id:"formSmash:j_idt720:0:j_idt724",widgetVar:"overlay1314811",target:"formSmash:j_idt720:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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