CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt146",{id:"formSmash:upper:j_idt146",widgetVar:"widget_formSmash_upper_j_idt146",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt147_j_idt149",{id:"formSmash:upper:j_idt147:j_idt149",widgetVar:"widget_formSmash_upper_j_idt147_j_idt149",target:"formSmash:upper:j_idt147:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Quotient complexes and lexicographic shellabilityPrimeFaces.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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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2002 (English)In: Journal of Algebraic Combinatorics, ISSN 0925-9899, E-ISSN 1572-9192, Vol. 16, no 1, 83-96 p.Article in journal (Refereed) Published
##### Abstract [en]

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

2002. Vol. 16, no 1, 83-96 p.
##### Keyword [en]

quotient complex, cell complex of boolean type, lexicographic shellability, coxeter subspace arrangement, homotopy, subspace arrangements, simplicial posets
##### Identifiers

URN: urn:nbn:se:kth:diva-22002ISI: 000178886000006OAI: oai:DiVA.org:kth-22002DiVA: diva2:340700
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt434",{id:"formSmash:j_idt434",widgetVar:"widget_formSmash_j_idt434",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt440",{id:"formSmash:j_idt440",widgetVar:"widget_formSmash_j_idt440",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt446",{id:"formSmash:j_idt446",widgetVar:"widget_formSmash_j_idt446",multiple:true});
##### Note

QC 20100525Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved

Let Pi(n,k,k) and Pi(n,k,h), h < k, denote the intersection lattices of the k-equal subspace arrangement of type D-n and the k, h-equal subspace arrangement of type B-n respectively. Denote by S-n(B) the group of signed permutations. We show that Delta(Pi(n,k,k))/S-n(B) is collapsible. For Delta(Pi(n,k,h))/S-n(B),h < k, we show the following. If n = 0 (mod k), then it is homotopy equivalent to a sphere of dimension 2n/k = 2. If n = h (mod k), then it is homotopy equivalent to a sphere of dimension 2n-h/k-1. Otherwise, it is contractible. Immediate consequences for the multiplicity of the trivial characters in the representations of S-n(B) on the homology groups of Delta(Pi(n,k,k)) and Delta(Pi(n,k,h)) are stated. The collapsibility of Delta (Pi(n,k,k))/S-n(B) is established using a discrete Morse function. The same method is used to show that Delta(Pi(n,k,h))/S-n(B), h < k, is homotopy equivalent to a certain subcomplex. The homotopy type of this subcomplex is calculated by showing that it is shellable. To do this, we are led to introduce a lexicographic shelling condition for balanced cell complexes of boolean type. This extends to the non-pure case work of P. Hersh (Preprint, 2001) and specializes to the CL-shellability of A. Bjorner and M. Wachs (Trans. Amer. Math. Soc. 4 (1996), 1299-1327) when the cell complex is an order complex of a poset.

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CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1197",{id:"formSmash:lower:j_idt1197",widgetVar:"widget_formSmash_lower_j_idt1197",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1198_j_idt1200",{id:"formSmash:lower:j_idt1198:j_idt1200",widgetVar:"widget_formSmash_lower_j_idt1198_j_idt1200",target:"formSmash:lower:j_idt1198:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});