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Annals of Combinatorics

, Volume 16, Issue 4, pp 789–813 | Cite as

On Intersection Lattices of Hyperplane Arrangements Generated by Generic Points

  • Hiroshi KoizumiEmail author
  • Yasuhide Numata
  • Akimichi Takemura
Article
  • 294 Downloads

Abstract

We consider hyperplane arrangements generated by generic points and study their intersection lattices. These arrangements are known to be equivalent to discriminantal arrangements. We show a fundamental structure of the intersection lattices by decomposing the poset ideals as direct products of smaller lattices corresponding to smaller dimensions. Based on this decomposition we compute the Möbius functions of the lattices and the characteristic polynomials of the arrangements up to dimension six.

Mathematics Subject Classification

52C35 05A99 

Keywords

discriminantal arrangements Möbius function characteristic polynomial enumeration of elements 

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Copyright information

© Springer Basel 2012

Authors and Affiliations

  • Hiroshi Koizumi
    • 1
    Email author
  • Yasuhide Numata
    • 1
  • Akimichi Takemura
    • 1
  1. 1.Mathematical InformaticsGraduate School of Information Science and Technology, Universityof TokyoTokyoJapan

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