Free filtrations of affine Weyl arrangements and the ideal-Shi arrangements

Takuro Abe, Hiroaki Terao

Research output: Contribution to journalArticle

7 Citations (Scopus)


In this article, we prove that the ideal-Shi arrangements are free central arrangements of hyperplanes satisfying the dual partition formula. Then, it immediately follows that there exists a saturated free filtration of the cone of any affine Weyl arrangement such that each subarrangement of the filtration satisfies the dual partition formula. This generalizes the main result in Abe et al. (J. Eur. Math. Soc., to appear) which affirmatively settled a conjecture by Sommers and Tymoczko (Trans. Am. Math. Soc. 358:3493–3509, 2006).

Original languageEnglish
Pages (from-to)33-44
Number of pages12
JournalJournal of Algebraic Combinatorics
Issue number1
Publication statusPublished - Feb 1 2016
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

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