Affine and toric hyperplane arrangements

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31 Citations (SciVal)


We extend the Billera-Ehrenborg-Readdy map between the intersection lattice and face lattice of a central hyperplane arrangement to affine and toric hyperplane arrangements. For arrangements on the torus, we also generalize Zaslavsky's fundamental results on the number of regions.

Original languageEnglish
Pages (from-to)481-512
Number of pages32
JournalDiscrete and Computational Geometry
Issue number4
StatePublished - Jun 2009


  • Flag enumeration
  • Manifolds
  • The cd-index
  • The complex of unbounded regions
  • The n-dimensional torus
  • The toric Zaslavsky invariant

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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