Affine and toric hyperplane arrangements

Richard Ehrenborg; Margaret Readdy; Michael Slone

doi:10.1007/s00454-009-9134-x

Affine and toric hyperplane arrangements

Richard Ehrenborg, Margaret Readdy, Michael Slone

Mathematics

Research output: Contribution to journal › Article › peer-review

32 Citations (SciVal)

Abstract

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 language	English
Pages (from-to)	481-512
Number of pages	32
Journal	Discrete and Computational Geometry
Volume	41
Issue number	4
DOIs	https://doi.org/10.1007/s00454-009-9134-x
State	Published - Jun 2009

Keywords

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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10.1007/s00454-009-9134-x

Cite this

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title = "Affine and toric hyperplane arrangements",

abstract = "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.",

keywords = "Flag enumeration, Manifolds, The cd-index, The complex of unbounded regions, The n-dimensional torus, The toric Zaslavsky invariant",

author = "Richard Ehrenborg and Margaret Readdy and Michael Slone",

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T1 - Affine and toric hyperplane arrangements

AU - Ehrenborg, Richard

AU - Readdy, Margaret

AU - Slone, Michael

PY - 2009/6

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N2 - 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.

AB - 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.

KW - Flag enumeration

KW - Manifolds

KW - The cd-index

KW - The complex of unbounded regions

KW - The n-dimensional torus

KW - The toric Zaslavsky invariant

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DO - 10.1007/s00454-009-9134-x

M3 - Article

AN - SCOPUS:63349098132

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SP - 481

EP - 512

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 4

ER -

Affine and toric hyperplane arrangements

Abstract

Keywords

ASJC Scopus subject areas

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