References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt145",{id:"formSmash:upper:j_idt145",widgetVar:"widget_formSmash_upper_j_idt145",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt146_j_idt148",{id:"formSmash:upper:j_idt146:j_idt148",widgetVar:"widget_formSmash_upper_j_idt146_j_idt148",target:"formSmash:upper:j_idt146:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Improving the bounds of the multiplicity conjecture: The codimension 3 level casePrimeFaces.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}); 2007 (English)In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 209, no 1, 79-89 p.Article in journal (Refereed) Published
##### Abstract [en]

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

2007. Vol. 209, no 1, 79-89 p.
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-37323DOI: 10.1016/j.jpaa.2006.05.017ISI: 000243862300005ScopusID: 2-s2.0-33751526061OAI: oai:DiVA.org:kth-37323DiVA: diva2:433165
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt375",{id:"formSmash:j_idt375",widgetVar:"widget_formSmash_j_idt375",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt381",{id:"formSmash:j_idt381",widgetVar:"widget_formSmash_j_idt381",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt387",{id:"formSmash:j_idt387",widgetVar:"widget_formSmash_j_idt387",multiple:true});
Available from: 2011-08-09 Created: 2011-08-09 Last updated: 2011-08-09Bibliographically approved

The Multiplicity Conjecture (MC) of Huneke and Srinivasan provides upper and lower bounds for the multiplicity of a Cohen-Macaulay algebra A in terms of the shifts appearing in the modules of the minimal free resolution (MFR) of A. All the examples studied so far have lead to conjecture (see [J. Herzog, X. Zheng, Notes on the multiplicity conjecture. Collect. Math. 57 (2006) 211-226] and [J. Mighore, U. Nagel, T. Romer, Extensions of the multiplicity conjecture, Trans. Amer. Math. Soc. (preprint: math. AC/0505229) (in press)]) that, moreover, the bounds of the MC are sharp if and only if A has a pure MFR. Therefore, it seems a reasonable - and useful - idea to seek better, if possibly ad hoc, bounds for particular classes of Cohen-Macaulay algebras. In this work we will only consider the codimension 3 case. In the first part we will stick to the bounds of the MC, and show that they hold for those algebras whose h-vector is that of a compressed algebra. In the second part, we will (mainly) focus on the level case: we will construct new conjectural upper and lower bounds for the multiplicity of a codimension 3 level algebra A, which can be expressed exclusively in terms of the h-vector of A, and which are better than (or equal to) those provided by the MC. Also, our bounds can be sharp even when the MFR of A is not pure. Even though proving our bounds still appears too difficult a task in general, we are already able to show them for some interesting classes of codimension 3 level algebras A: namely, when A is compressed, or when its h-vector h(A) ends with (.., 3, 2). Also, we will prove our lower bound when h(A) begins with (1, 3, h,), where h(2) : 4, and our upper bound when h (A) ends with (.... h(c-1), h(c)), where h(c-1) < h(c) + 1.

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1080",{id:"formSmash:lower:j_idt1080",widgetVar:"widget_formSmash_lower_j_idt1080",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1081_j_idt1083",{id:"formSmash:lower:j_idt1081:j_idt1083",widgetVar:"widget_formSmash_lower_j_idt1081_j_idt1083",target:"formSmash:lower:j_idt1081:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});