4 citations · 8 across the 11 of their papers we have counts for
12 papers
Characteristic quasi-polynomials for deformations of Coxeter arrangements of types A, B, C, and D
Yusuke Mori, Norihiro Nakashima
Kamiya, Takemura, and Terao introduced a characteristic quasi-polynomial which enumerates the numbers of elements in the complement of hyperplane arrangements modulo positive integ…
Freeness for restriction arrangements of the extended Shi and Catalan arrangements
Norihiro Nakashima, Shuhei Tsujie
The extended Shi and Catalan arrangements are well investigated arrangements. In this paper, we prove that the cone of the extended Catalan arrangement of type A is always heredita…
Enumeration of Flats of the Extended Catalan and Shi Arrangements with Species
Norihiro Nakashima, Shuhei Tsujie
The number of flats of a hyperplane arrangement is considered as a generalization of the Bell number and the Stirling number of the second kind. Robert Gill gave the exponential ge…
High order free hyperplane arrangements in 3-dimensional vector spaces
Norihiro Nakashima
Holm introduced -free -arrangements which is a generalization of free arrangements, while he asked whether all -arrangements are -free for large enough. Recen…
A characterization of high order freeness for product arrangements and answers to Holm's questions
Takuro Abe, Norihiro Nakashima
An m-free hyperplane arrangement is a generalization of a free arrangement. Holm asked the following two questions: (1)Does m-free imply (m+1)-free for any arrangement? (2)Are all…
Decoding of Projective Reed-Muller Codes by Dividing a Projective Space into Affine Spaces
Norihiro Nakashima, Hajime Matsui
A projective Reed-Muller (PRM) code, obtained by modifying a (classical) Reed-Muller code with respect to a projective space, is a doubly extended Reed-Solomon code when the dimens…
Canonical systems of basic invariants for unitary reflection groups
Norihiro Nakashima, Hiroaki Terao, Shuhei Tsujie
It has been known that there exists a canonical system for every finite real reflection group. The first and the third authors obtained an explicit formula for a canonical system i…
Distribution of accumulation points of roots for type Coxeter groups
Akihiro Higashitani, Ryosuke Mineyama, Norihiro Nakashima
In this paper, we investigate the set of accumulation points of normalized roots of infinite Coxeter groups for certain class of their action. Concretely, we prove the conjecture p…
A canonical system of basic invariants of a finite reflection group
Norihiro Nakashima, Shuhei Tsujie
A canonical system of basic invariants is a system of invariants satisfying a set of differential equations. The properties of a canonical system are related to the mean value prop…
Modules of differential operators of order 2 on Coxeter arrangements
Norihiro Nakashima
We prove that the modules of differential operators of order 2 on the classical Coxeter arrangements are free by exhibiting bases. For this purpose, we use Cauchy-Sylvester's theor…
The Freeness and Minimal Free Resolutions of Modules of Differential Operators of a Generic Hyperplane Arrangement
Norihiro Nakashima, Go Okuyama, Mutsumi Saito
Let A be a generic hyperplane arrangement composed of r hyperplanes in an n-dimensional vector space, and S the polynomial ring in n variables. We consider the S-submodule D(m)(A)…
The noetherian properties of the rings of differential operators on central 2-arrangements
Norihiro Nakashima
Whereas Holm proved that the ring of differential operators on a generic hyperplane arrangement is finitely generated as an algebra, the problem of its Noetherian properties is sti…