Inequalities for the h-Vectors and Flag h-Vectors of Geometric Lattices (English)

In: Discrete & Computational Geometry   ;  32 ,  4  ;  533-548  ;  2004

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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)).

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435
Guest Editors#8217 Preface
Bayer, Margaret M. / Lee, Carl W. / Sturmfels, Bernd | 2004
435
Guest Editors’ Preface
Bayer, Margaret M. / Lee, Carl W. / Sturmfels, Bernd | 2004
437
The Partial-Fractions Method for Counting Solutions to Integral Linear Systems
Beck, Matthias | 2004
447
Isoradial Bodies
Brandenberg, René / Dattasharma, Abhi / Gritzmann, Peter / Larman, David | 2004
459
Vertices of Gelfand--Tsetlin Polytopes
Loera, Jesús A. / McAllister, Tyrrell B. | 2004
471
A Complexity Bound on Faces of the Hull Complex
Develin, Mike | 2004
481
Enumerative Properties of Ferrers Graphs
Ehrenborg, Richard / Willigenburg, Stephanie | 2004
493
Tchebyshev Posets
Hetyei, Gábor | 2004
521
Mixed Fibre Polytopes
McMullen, Peter | 2004
533
Inequalities for the h-Vectors and Flag h-Vectors of Geometric Lattices
Nyman, Kathryn / Swartz, Ed | 2004
549
Convex Combinatorial Optimization
Onn, Shmuel / Rothblum, Uriel G. | 2004
567
Non-Crossing Frameworks with Non-Crossing Reciprocals
Orden, David / Rote, Günter / Santos, Francisco / Servatius, Brigitte / Servatius, Herman / Whiteley, Walter | 2004
601
The Et-Construction for Lattices, Spheres and Polytopes
Paffenholz, Andreas / Ziegler, Günter M. | 2004
623
Graphs, Syzygies, and Multivariate Splines
Rose, Lauren L. | 2004
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