CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt165",{id:"formSmash:upper:j_idt165",widgetVar:"widget_formSmash_upper_j_idt165",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt166_j_idt168",{id:"formSmash:upper:j_idt166:j_idt168",widgetVar:"widget_formSmash_upper_j_idt166_j_idt168",target:"formSmash:upper:j_idt166:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Generalised Ramsey numbers and Bruhat order on involutionsPrimeFaces.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();
}
}
PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2015 (English)Licentiate thesis, comprehensive summary (Other academic)
##### Abstract [en]

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

Linköping: Linköping University Electronic Press, 2015. , 14 p.
##### Series

Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1734
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:liu:diva-123044DOI: 10.3384/lic.diva-123044ISBN: 978-91-7685-892-9 (print)OAI: oai:DiVA.org:liu-123044DiVA: diva2:876270
##### Presentation

2015-12-17, Nobel (BL32), ingång 23, B-huset, Campus Valla, Linköpings universitet, Linköping, 10:15 (Swedish)
##### Opponent

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt476",{id:"formSmash:j_idt476",widgetVar:"widget_formSmash_j_idt476",multiple:true});
##### Supervisors

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt482",{id:"formSmash:j_idt482",widgetVar:"widget_formSmash_j_idt482",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt488",{id:"formSmash:j_idt488",widgetVar:"widget_formSmash_j_idt488",multiple:true});
Available from: 2015-12-03 Created: 2015-12-03 Last updated: 2015-12-03Bibliographically approved
##### List of papers

This thesis consists of two papers within two different areas of combinatorics.

Ramsey theory is a classic topic in graph theory, and Paper A deals with two of its most fundamental problems: to compute Ramsey numbers and to characterise critical graphs. More precisely, we study generalised Ramsey numbers for two sets Γ_{1} and Γ_{2} of cycles. We determine, in particular, all generalised Ramsey numbers R(Γ_{1}, Γ_{2}) such that Γ_{1} or Γ_{2} contains a cycle of length at most 6, or the shortest cycle in each set is even. This generalises previous results of Erdös, Faudree, Rosta, Rousseau, and Schelp. Furthermore, we give a conjecture for the general case. We also characterise many (Γ_{1}, Γ_{2})-critical graphs. As special cases, we obtain complete characterisations of all (C_{n},C_{3})-critical graphs for n ≥ 5, and all (C_{n},C_{5})-critical graphs for n ≥ 6.

In Paper B, we study the combinatorics of certain partially ordered sets. These posets are unions of conjugacy classes of involutions in the symmetric group S_{n}, with the order induced by the Bruhat order on S* _{n}*. We obtain a complete characterisation of the posets that are graded. In particular, we prove that the set of involutions with exactly one fixed point is graded, which settles a conjecture of Hultman in the affirmative. When the posets are graded, we give their rank functions. We also give a short, new proof of the EL-shellability of the set of fixed-point-free involutions, recently proved by Can, Cherniavsky, and Twelbeck.

1. Generalised Ramsey numbers for two sets of cycles$(function(){PrimeFaces.cw("OverlayPanel","overlay876248",{id:"formSmash:j_idt524:0:j_idt530",widgetVar:"overlay876248",target:"formSmash:j_idt524:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. The Bruhat order on conjugation-invariant sets of involutions in the symmetric group$(function(){PrimeFaces.cw("OverlayPanel","overlay876258",{id:"formSmash:j_idt524:1:j_idt530",widgetVar:"overlay876258",target:"formSmash:j_idt524:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
isbn
urn-nbn$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_j_idt1204",{id:"formSmash:j_idt1204",widgetVar:"widget_formSmash_j_idt1204",showEffect:"fade",hideEffect:"fade",showDelay:500,hideDelay:300,target:"formSmash:altmetricDiv"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1257",{id:"formSmash:lower:j_idt1257",widgetVar:"widget_formSmash_lower_j_idt1257",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1258_j_idt1260",{id:"formSmash:lower:j_idt1258:j_idt1260",widgetVar:"widget_formSmash_lower_j_idt1258_j_idt1260",target:"formSmash:lower:j_idt1258:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});