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Discrete & Computational Geometry

, Volume 32, Issue 4, pp 533–548 | Cite as

Inequalities for the h-Vectors and Flag h-Vectors of Geometric Lattices

  • Kathryn Nyman
  • Ed Swartz
Article

Abstract

We prove that the order complex of a geometric lattice has a convex ear decomposition. As a consequence, if Δ(L) is the order complex of a rank (r + 1) geometric lattice L, then for all i ≤ r/2 the h-vector of Δ(L) satisfies hi-1 ≤ hi and hi ≤ hr-i. We also obtain several inequalities for the flag h-vector of Δ(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 hi-1 ≤ hi when i ≤ (2/7)(r + (5/2)).

Keywords

Computational Mathematic Symmetric Group Order Complex Bruhat Order Geometric Lattice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer 2004

Authors and Affiliations

  1. 1.Department of Mathematics, Loyola University Chicago, Chicago, IL 60626USA
  2. 2.Department of Mathematics, Cornell University, Ithaca, NY 14853USA

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