CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt828",{id:"formSmash:upper:j_idt828",widgetVar:"widget_formSmash_upper_j_idt828",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt829_j_idt831",{id:"formSmash:upper:j_idt829:j_idt831",widgetVar:"widget_formSmash_upper_j_idt829_j_idt831",target:"formSmash:upper:j_idt829:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

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});
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();
}
}
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
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt1118",{id:"formSmash:j_idt1118",widgetVar:"widget_formSmash_j_idt1118",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt1124",{id:"formSmash:j_idt1124",widgetVar:"widget_formSmash_j_idt1124",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt1130",{id:"formSmash:j_idt1130",widgetVar:"widget_formSmash_j_idt1130",multiple:true});
##### 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_idt1404:0:j_idt1408",widgetVar:"overlay1314811",target:"formSmash:j_idt1404:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
urn-nbn$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_j_idt1840",{id:"formSmash:j_idt1840",widgetVar:"widget_formSmash_j_idt1840",showEffect:"fade",hideEffect:"fade",showDelay:500,hideDelay:300,target:"formSmash:altmetricDiv"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1893",{id:"formSmash:lower:j_idt1893",widgetVar:"widget_formSmash_lower_j_idt1893",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1894_j_idt1896",{id:"formSmash:lower:j_idt1894:j_idt1896",widgetVar:"widget_formSmash_lower_j_idt1894_j_idt1896",target:"formSmash:lower:j_idt1894:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});