The freeness of ideal subarrangements of Weyl arrangements

Autor: Takuro Abe, Mohamed Barakat, Michael Cuntz, Torsten Hoge, Hiroaki Terao

Publikováno v: Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings vol. AT,..., Iss Proceedings (2014)

A Weyl arrangement is the arrangement defined by the root system of a finite Weyl group. When a set of positive roots is an ideal in the root poset, we call the corresponding arrangement an ideal subarrangement. Our main theorem asserts that any idea

Externí odkaz: https://doaj.org/article/f0277c8030d84dfeb8609c049b18d8ee

Logarithmic vector fields for curve configurations in $\mathbb{P}^2$ with quasihomogeneous singularities

Autor: Hal Schenck, Hiroaki Terao, Masahiko Yoshinaga

Publikováno v: Mathematical Research Letters. 25:1977-1992

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::23dc85099437c9da4faa70a439a58827
https://doi.org/10.4310/mrl.2018.v25.n6.a14

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

Autor: Takuro Abe, Hiroaki Terao

Publikováno v: Journal of Algebraic Combinatorics. 43:33-44

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 ar

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9bdcdaacf81d8742b24b7d579727810d
https://doi.org/10.1007/s10801-015-0624-z

The freeness of ideal subarrangements of Weyl arrangements

Autor: Torsten Hoge, Mohamed Barakat, Takuro Abe, Hiroaki Terao, Michael Cuntz

Publikováno v: Discrete Mathematics and Theoretical Computer Science
26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.501-512
Journal of the European Mathematical Society 18 (2016), Nr. 6

A Weyl arrangement is the arrangement defined by the root system of a finite Weyl group. When a set of positive roots is an ideal in the root poset, we call the corresponding arrangement an ideal subarrangement. Our main theorem asserts that any idea

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fad43005b84879fe89c82d114a64b147

Periodicity of Non-Central Integral Arrangements Modulo Positive Integers

Autor: Hidehiko Kamiya, Hiroaki Terao, Akimichi Takemura

Publikováno v: Annals of Combinatorics. 15:449-464

An integral coefficient matrix determines an integral arrangement of hyperplanes in $${\mathbb{R}^m}$$ . After modulo q reduction $${(q \in {\mathbb{Z}_{ >0 }})}$$ , the same matrix determines an arrangement $${\mathcal{A}_q}$$ of “hyperplanes” i

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fc1f99d532865094280dc79bcbee1bf2
https://doi.org/10.1007/s00026-011-0105-6