Abstract
A Weyl arrangement is the hyperplane arrangement defined by a root system. Saito proved that every Weyl arrangement is free. The Weyl subarrangements of type [Formula presented] are represented by simple graphs. Stanley gave a characterization of freeness for this type of arrangements in terms of their graph. In addition, the Weyl subarrangements of type [Formula presented] can be represented by signed graphs. A characterization of freeness for them is not known. However, characterizations of freeness for a few restricted classes are known. For instance, Edelman and Reiner characterized the freeness of the arrangements between type [Formula presented] and type [Formula presented]. In this paper, we give a characterization of the freeness and supersolvability of the Weyl subarrangements of type [Formula presented] under certain assumption.
Original language | English (US) |
---|---|
Pages (from-to) | 233-249 |
Number of pages | 17 |
Journal | Discrete Mathematics |
Volume | 342 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2019 |
Externally published | Yes |
Keywords
- Chordal graph
- Free arrangement
- Graphic arrangement
- Hyperplane arrangement
- Signed graph
- Supersolvable arrangement
- Weyl arrangement
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics