Signed graphs and the freeness of the Weyl subarrangements of type [Formula presented]

Daisuke Suyama, Michele Torielli, Shuhei Tsujie

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

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 languageEnglish (US)
Pages (from-to)233-249
Number of pages17
JournalDiscrete Mathematics
Volume342
Issue number1
DOIs
StatePublished - Jan 2019
Externally publishedYes

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

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