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- Title
On Intersection Lattices of Hyperplane Arrangements Generated by Generic Points.
- Authors
Koizumi, Hiroshi; Numata, Yasuhide; Takemura, Akimichi
- 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.
- Subjects
INTERSECTION theory; LATTICE theory; HYPERPLANES; MOBIUS function; POLYNOMIALS; MATHEMATICAL decomposition; DIMENSION theory (Algebra); IDEALS (Algebra)
- Publication
Annals of Combinatorics, 2012, Vol 16, Issue 4, p789
- ISSN
0218-0006
- Publication type
Article
- DOI
10.1007/s00026-012-0161-6