Intersections of Apartments

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dc.creatorAbramenko, Peter
dc.creatorVan Maldeghem, Hendrik
dc.date2008-05-28
dc.date.accessioned2026-07-07T09:41:33Z
dc.date.available2026-07-07T09:41:33Z
dc.descriptionWe show that, if a building is endowed with its complete system of apartments, and if each panel is contained in at least four chambers, then the intersection of two apartments can be any convex subcomplex contained in an apartment. This combinatorial result is particularly interesting for lower dimensional convex subcomplexes of apartments, where we definitely need the assumption on the four chambers per panel in the building. The corresponding statement is not true anymore for arbitrary systems of apartments, and counter-examples for infinite convex subcomplexes exist for any type of buildings. However, when we restrict to finite convex subcomplexes, the above remains true for arbitrary systems of apartments if and only if every finite subset of chambers of the standard Coxeter complex is contained in the convex hull of two chambers.
dc.description22 pages, combinatorial building theory, simplicial and W-metric approach
dc.identifierhttps://arxiv.org/abs/0805.4442
dc.identifierhttp://arxiv.org/abs/0805.4442
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161864
dc.subjectCombinatorics
dc.subjectGroup Theory
dc.subject51E24; 20E42
dc.titleIntersections of Apartments
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