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Multivariate P-Eulerian 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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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); (English)Manuscript (preprint) (Other academic)
##### Abstract [en]

##### National Category

Mathematics
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:su:diva-128347OAI: oai:DiVA.org:su-128347DiVA: diva2:914224
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt434",{id:"formSmash:j_idt434",widgetVar:"widget_formSmash_j_idt434",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt440",{id:"formSmash:j_idt440",widgetVar:"widget_formSmash_j_idt440",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt446",{id:"formSmash:j_idt446",widgetVar:"widget_formSmash_j_idt446",multiple:true});
Available from: 2016-03-23 Created: 2016-03-23 Last updated: 2016-04-22Bibliographically approved
##### In thesis

The P-Eulerian polynomial counts the linear extensions of a labeled partially ordered set, P, by their number of descents. It is known that the P-Eulerian polynomials are real-rooted for various classes of posets P. The purpose of this paper is to extend these results to polynomials in several variables. To this end we study multivariate extensions of P-Eulerian polynomials and prove that for certain posets these polynomials are stable, i.e., non-vanishing whenever all variables are in the upper half-plane of the complex plane. A natural setting for our proofs is the Malvenuto-Reutenauer algebra of permutations (or the algebra of free quasi-symmetric functions). In the process we identify an algebra on Dyck paths, which to our knowledge has not been studied before.

1. Combinatorics of stable polynomials and correlation inequalities$(function(){PrimeFaces.cw("OverlayPanel","overlay915712",{id:"formSmash:j_idt707:0:j_idt711",widgetVar:"overlay915712",target:"formSmash:j_idt707:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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