Inequalities for the h- and flag h-vectors of geometric lattices

dc.creatorNyman, Kathryn
dc.creatorSwartz, Ed
dc.date2004-05-27
dc.date2005-02-18
dc.date.accessioned2026-07-07T05:08:39Z
dc.date.available2026-07-07T05:08:39Z
dc.descriptionWe prove that the order complex of a geometric lattice has a convex ear decomposition. As a consequence, if D(L) is the order complex of a rank (r+1) geometric lattice L, then for all i \leq r/2 the h-vector of D(L) satisfies h(i-1) \leq h(i) and h(i) \leq h(r-i). We also obtain several inequalities for the flag h-vector of D(L) by analyzing the weak Bruhat order of the symmetric group. As an application, we obtain a zonotopal cd-analogue of the Dowling-Wilson characterization of geometric lattices which minimize Whitney numbers of the second kind. In addition, we are able to give a combinatorial flag h-vector proof of h(i-1) \leq h(i) when i \leq (2/7)(r + 5/2).
dc.description15 pages, 2 figures. Typos fixed; most notably in Table 1. A note was added regarding a solution to problem 4.6
dc.identifierhttps://arxiv.org/abs/math/0405535
dc.identifierhttp://arxiv.org/abs/math/0405535
dc.identifierDiscrete and Computational Geometry, Vol. 32, No. 4, Nov. 2004, pgs 533-548
dc.identifierdoi:10.1007/s00454-004-1137-z
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71354
dc.subjectCombinatorics
dc.subject06C10
dc.titleInequalities for the h- and flag h-vectors of geometric lattices
dc.typetext

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