The Et-Construction for Lattices, Spheres and Polytopes (English)

In: Discrete & Computational Geometry   ;  32 ,  4  ;  601-621  ;  2004

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Abstract We describe and analyze a new construction that produces new Eulerian lattices from old ones. It specializes to a construction that produces new strongly regular cellular spheres (whose face lattices are Eulerian). The construction does not always specialize to convex polytopes; however, in a number of cases where we can realize it, it produces interesting classes of polytopes. Thus we produce an infinite family of rational 2-simplicial 2-simple 4-polytopes, as requested by Eppstein et al. We also construct for each d ≥ 3 an infinite family of (d – 2)-simplicial 2-simple d-polytopes, thus solving a problem of Grünbaum.

Table of contents – Volume 32, Issue 4

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435
Guest Editors’ Preface
Bayer, Margaret M. / Lee, Carl W. / Sturmfels, Bernd | 2004
435
Guest Editors#8217 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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