The Dowling transform of subspace arrangements
type: Item
instance of: scholarly article
title: The Dowling transform of subspace arrangements
zbMATH Open document ID: 0962.05005
author: Richard Ehrenborg
author: Margaret A. Readdy
published in: Journal of Combinatorial Theory. Series A
publication date: 2001-06-13T00:00:00Z
review text: The paper introduces the Dowling transform, which takes a real frame arrangement with coordinate hyperplanes into a complex one. The Dowling transform takes the braid arrangement \(A_n\) to the Dowling arrangement. It is shown that the Dowling transform preserves supersolvability. A direct proof is given to Zaslavsky's theorem, which counts the chambers and bounded chambers of a real hyperplane arrangement in terms of the characteristic polynomial of the arrangement.
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 52C35
zbMATH DE Number: 1525312
zbMATH Keywords: valuations
zbMATH Keywords: intersection lattice
zbMATH Keywords: frame arrangement
zbMATH Keywords: Dowling transform
zbMATH Keywords: braid arrangement
zbMATH Keywords: supersolvability
zbMATH Keywords: hyperplane arrangement
zbMATH Keywords: characteristic polynomial
reviewed by: László A. Székely
MaRDI profile type: Publication
OpenAlex ID: W2163320675
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DOI: 10.1006/JCTA.2000.3098
description: scientific article; zbMATH DE number 1525312