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The cone of cyclic sieving phenomenaPrimeFaces.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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2019 (English)In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 342, no 6, p. 1581-1601Article in journal (Refereed) Published
##### Abstract [en]

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

Elsevier, 2019. Vol. 342, no 6, p. 1581-1601
##### Keywords [en]

cyclic sieving, stretched schur polynomial, convex polytope
##### National Category

Discrete Mathematics
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-250764DOI: 10.1016/j.disc.2019.01.037ISI: 000466833400006Scopus ID: 2-s2.0-85062678575OAI: oai:DiVA.org:kth-250764DiVA, id: diva2:1313631
#####

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##### Note

##### In thesis

We study cyclic sieving phenomena (CSP) on combinatorial objects from an abstract point of view by considering a rational polyhedral cone determined by the linear equations that define such phenomena. Each lattice point in the cone corresponds to a non-negative integer matrix which jointly records the statistic and cyclic order distribution associated with the set of objects realizing the CSP. In particular we consider a *universal* subcone onto which every CSP matrix linearly projects such that the projection realizes a CSP with the same cyclic orbit structure, but via a *universal *statistic that has even distribution on the orbits.

Reiner et.al. showed that every cyclic action gives rise to a unique polynomial (mod q^n-1) complementing the action to a CSP. We give a necessary and sufficient criterion for the converse to hold. This characterization allows one to determine if a combinatorial set with a statistic gives rise (in principle) to a CSP without having a combinatorial realization of the cyclic action. We apply the criterion to conjecture a new CSP involving stretched Schur polynomials and prove our conjecture for certain rectangular tableaux. Finally we study some geometric properties of the CSP cone. We explicitly determine its half-space description and in the prime order case we determine its extreme rays.

QC 20190510

Available from: 2019-05-05 Created: 2019-05-05 Last updated: 2019-05-29Bibliographically approved1. Combinatorics and zeros of multivariate polynomials$(function(){PrimeFaces.cw("OverlayPanel","overlay1314811",{id:"formSmash:j_idt1181:0:j_idt1185",widgetVar:"overlay1314811",target:"formSmash:j_idt1181:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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