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The Dowling Transform of Subspace Arrangements

✍ Scribed by Richard Ehrenborg; Margaret A. Readdy

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
121 KB
Volume
91
Category
Article
ISSN
0097-3165

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✦ Synopsis

We define the Dowling transform of a real frame arrangement and show how the characteristic polynomial changes under this transformation. As a special case, the Dowling transform sends the braid arrangement A n to the Dowling arrangement. Using Zaslavsky's characterization of supersolvability of signed graphs, we show supersolvability of an arrangement is preserved under the Dowling transform. We also give a direct proof of Zaslavsky's result on the number of chambers and bounded chambers in a real hyperplane arrangement.

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