7 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…
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)…