liu.seSearch for publications in DiVA

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt169",{id:"formSmash:upper:j_idt169",widgetVar:"widget_formSmash_upper_j_idt169",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt171_j_idt173",{id:"formSmash:upper:j_idt171:j_idt173",widgetVar:"widget_formSmash_upper_j_idt171_j_idt173",target:"formSmash:upper:j_idt171:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

The Bruhat order on conjugation-invariant sets of involutions in the symmetric groupPrimeFaces.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();
}
}
2016 (English)In: Journal of Algebraic Combinatorics, ISSN 0925-9899, E-ISSN 1572-9192, Vol. 44, no 4, p. 849-862Article in journal (Refereed) Published
##### Abstract [en]

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

Springer, 2016. Vol. 44, no 4, p. 849-862
##### Keywords [en]

Bruhat order, symmetric group, involution, conjugacy class, graded poset, EL-shellability
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:liu:diva-123043DOI: 10.1007/s10801-016-0691-9ISI: 000387223300002OAI: oai:DiVA.org:liu-123043DiVA, id: diva2:876258
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt581",{id:"formSmash:j_idt581",widgetVar:"widget_formSmash_j_idt581",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt588",{id:"formSmash:j_idt588",widgetVar:"widget_formSmash_j_idt588",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt595",{id:"formSmash:j_idt595",widgetVar:"widget_formSmash_j_idt595",multiple:true});
##### Note

##### In thesis

Let *I*_{n} be the set of involutions in the symmetric group *S*_{n}, and for *A* {0, 1, . . . , *n*}, let

= { *I*_{n} | has *α* fixed points for some *α* *A*}.

We give *a* complete characterisation of the sets *A* for which , with the order induced by the Bruhat order on S_{n}, is a graded poset. In particular, we prove that (i.e., the set of involutions with exactly one fixed point) is graded, which settles a conjecture of Hultman in the affirmative. When is graded, we give its rank function. We also give a short, new proof of the EL-shellability of (i.e., the set of fixed-point-free involutions), recently proved by Can, Cherniavsky, and Twelbeck.

At the time for thesis presentation publication was in status: Manuscript

Available from: 2015-12-03 Created: 2015-12-03 Last updated: 2018-05-21Bibliographically approved1. Generalised Ramsey numbers and Bruhat order on involutions$(function(){PrimeFaces.cw("OverlayPanel","overlay876270",{id:"formSmash:j_idt902:0:j_idt906",widgetVar:"overlay876270",target:"formSmash:j_idt902:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Combinatorics and topology related to involutions in Coxeter groups$(function(){PrimeFaces.cw("OverlayPanel","overlay1208893",{id:"formSmash:j_idt902:1:j_idt906",widgetVar:"overlay1208893",target:"formSmash:j_idt902:1:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
urn-nbn$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_j_idt1649",{id:"formSmash:j_idt1649",widgetVar:"widget_formSmash_j_idt1649",showEffect:"fade",hideEffect:"fade",showDelay:500,hideDelay:300,target:"formSmash:altmetricDiv"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1709",{id:"formSmash:lower:j_idt1709",widgetVar:"widget_formSmash_lower_j_idt1709",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1710_j_idt1712",{id:"formSmash:lower:j_idt1710:j_idt1712",widgetVar:"widget_formSmash_lower_j_idt1710_j_idt1712",target:"formSmash:lower:j_idt1710:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});