The Dowling transform of subspace arrangements

Richard Ehrenborg; Margaret A. Readdy

doi:10.1006/jcta.2000.3098

The Dowling transform of subspace arrangements

Mathematics

Producción científica: Article › revisión exhaustiva

5 Citas (Scopus)

Resumen

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.

Idioma original	English
Páginas (desde-hasta)	322-333
Número de páginas	12
Publicación	Journal of Combinatorial Theory. Series A
Volumen	91
N.º	1-2
DOI	https://doi.org/10.1006/jcta.2000.3098
Estado	Published - jul 2000

Nota bibliográfica

Funding Information:
The authors thank MIT, where as visiting scholars they completed some of this work and the Institute for Advanced Study, where this work was continued while both authors were members. The first author was supported by the National Science Foundation, under Grant DMS 97-29992, and the NEC Research Institute, Inc., while at the Institute for Advanced Study.

Financiación

The authors thank MIT, where as visiting scholars they completed some of this work and the Institute for Advanced Study, where this work was continued while both authors were members. The first author was supported by the National Science Foundation, under Grant DMS 97-29992, and the NEC Research Institute, Inc., while at the Institute for Advanced Study.

Financiadores	Número del financiador
National Science Foundation (NSF)	DMS 97-29992

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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note = "Funding Information: The authors thank MIT, where as visiting scholars they completed some of this work and the Institute for Advanced Study, where this work was continued while both authors were members. The first author was supported by the National Science Foundation, under Grant DMS 97-29992, and the NEC Research Institute, Inc., while at the Institute for Advanced Study.",

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N2 - 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 An 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.

AB - 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 An 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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The Dowling transform of subspace arrangements

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

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