6 papers · 1 filter
Equivariant version of the characteristic quasi-polynomials of root systems
Ryo Uchiumi
An equivariant characteristic quasi-polynomial is a quasi-polynomial in consisting of the permutation character on the mod complement of the corresponding Coxeter arrangeme…
Root systems constructed by folding of the extended Dynkin diagrams
Ryo Uchiumi
The extended affine Weyl group of a root system is the semidirect product of the corresponding Weyl group by its coweight lattice. The stabilizer subgroup of the extended affine We…
The characteristic quasi-polynomials of hyperplane arrangements with actions of finite groups
Ryo Uchiumi
In this paper, we introduce an equivariant version of the characteristic quasi-polynomials as the permutation characters on the complement of mod hyperplane arrangements. We pr…
Exponents of 2-multiarrangements of three lines over fields of positive characteristic
Shuhei Tsujie, Ryo Uchiumi
Wakamiko determined bases and the exponents for multiarrangements of three lines over a field of characteristic zero. In this paper, we study the exponents of multiarrangements of…
-deformation of chromatic polynomials and graphical arrangements
Tongyu Nian, Shuhei Tsujie, Ryo Uchiumi +1
We first observe a mysterious similarity between the braid arrangement and the arrangement of all hyperplanes in a vector space over the finite field . These two arra…
The quasi-polynomiality of mod q permutation representation for a linear finite group action on a lattice
Ryo Uchiumi, Masahiko Yoshinaga
For given linear action of a finite group on a lattice and a positive integer q, we prove that the mod q permutation representation is a quasi-polynomial in q. Additionally, we est…