Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 322-333 |
| Number of pages | 12 |
| Journal | Journal of Combinatorial Theory. Series A |
| Volume | 91 |
| Issue number | 1-2 |
| DOIs | |
| State | Published - Jul 2000 |
Bibliographical 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.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics