3 papers
math.CO2024
Worpitzky-compatible sets and the freeness of arrangements between Shi and Catalan
Takuro Abe, Tan Nhat Tran
Given an irreducible root system, the Worpitzky-compatible subsets are defined by a geometric property of the alcoves inside the fundamental parallelepiped of the root system. This…
math.CO2023
A type analog of Ish arrangement
Tan Nhat Tran, Shuhei Tsujie
The Shi arrangement due to Shi (1986) and the Ish arrangement due to Armstrong (2013) are deformations of the type Coxeter arrangement that share many common properties. Motiva…
math.CO2023
Flag-accurate arrangements
Paul Mücksch, Gerhard Roehrle, Tan Nhat Tran
In [MR21], the first two authors introduced the notion of an accurate arrangement, a particular notion of freeness. In this paper, we consider a special subclass, where the propert…