Abstract
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).
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Acknowledgments
The first author is partially supported by JSPS Grants-in-Aid for Young Scientists (B) No. 24740012. The second author is partially supported by JSPS Grants-in-Aid for Scientific Research (A) No. 24244001.
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Abe, T., Terao, H. Free filtrations of affine Weyl arrangements and the ideal-Shi arrangements. J Algebr Comb 43, 33–44 (2016). https://doi.org/10.1007/s10801-015-0624-z
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DOI: https://doi.org/10.1007/s10801-015-0624-z