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).
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Discrete Mathematics and Combinatorics