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Discrete & Computational Geometry

, Volume 21, Issue 3, pp 389–403 | Cite as

On Flag Vectors, the Dowling Lattice, and Braid Arrangements

  • R. Ehrenborg
  • M. A. Readdy

Abstract.

We study complex hyperplane arrangements whose intersection lattices, known as the Dowling lattices, are a natural generalization of the partition lattice. We give a combinatorial description of the Dowling lattice via enriched partitions to obtain an explicit EL -labeling and then find a recursion for the flag h -vector in terms of weighted derivations. When the hyperplane arrangements are real they correspond to the braid arrangements A n and B n . By applying a result due to Billera and the authors, we obtain a recursive formula for the cd-index of the lattice of regions of the braid arrangements A n and B n .

Keywords

Natural Generalization Recursive Formula Intersection Lattice Hyperplane Arrangement Combinatorial Description 
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-Verlag New York Inc. 1999

Authors and Affiliations

  • R. Ehrenborg
    • 1
  • M. A. Readdy
    • 1
  1. 1.Department of Mathematics, Cornell University, White Hall, Ithaca, NY 14853-7901, USA jrge@math.cornell.edu, readdy@math.cornell.eduUS

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