Inequalities for the h- and flag h-vectors of geometric lattices
| dc.creator | Nyman, Kathryn | |
| dc.creator | Swartz, Ed | |
| dc.date | 2004-05-27 | |
| dc.date | 2005-02-18 | |
| dc.date.accessioned | 2026-07-07T05:08:39Z | |
| dc.date.available | 2026-07-07T05:08:39Z | |
| dc.description | We 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.description | 15 pages, 2 figures. Typos fixed; most notably in Table 1. A note was added regarding a solution to problem 4.6 | |
| dc.identifier | https://arxiv.org/abs/math/0405535 | |
| dc.identifier | http://arxiv.org/abs/math/0405535 | |
| dc.identifier | Discrete and Computational Geometry, Vol. 32, No. 4, Nov. 2004, pgs 533-548 | |
| dc.identifier | doi:10.1007/s00454-004-1137-z | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71354 | |
| dc.subject | Combinatorics | |
| dc.subject | 06C10 | |
| dc.title | Inequalities for the h- and flag h-vectors of geometric lattices | |
| dc.type | text |