Vincent Umutabazi

activity

20172023

collaborators

5 papers

math.CO2023

Fixed elements of pircon automorphisms

Mikael Hansson, Vincent Umutabazi

We prove that the subposet induced by the fixed elements of any automorphism of a pircon is also a pircon. By a result of Abdallah, Hansson, and Hultman, the order complex of any o…

math.CO2022

Zircons and smooth Bruhat intervals in symmetric groups

Vincent Umutabazi

In this paper, we prove that if the dual of a Bruhat interval in a Weyl group is a zircon, then that interval is rationally smooth. Investigating when the converse holds, and drawi…

math.CO2021

Boolean complexes of involutions

Axel Hultman, Vincent Umutabazi

Let (W,S) be a Coxeter system. We introduce the boolean complex of involutions of W which is an analogue of the boolean complex of W studied by Ragnarsson and Tenner. By applying d…

math.CO2019

Smoothness of Schubert varieties indexed by involutions in finite simply laced types

Axel Hultman, Vincent Umutabazi

We prove that in finite, simply laced types, every Schubert variety indexed by an involution which is not the longest element of some parabolic subgroup is singular.

math.AC2017

Red-injective modules

Juma Kasozi, David Ssevviiri, Vincent Umutabazi

Let $Red (M)$ be the sum of all reduced submodules of a module $M$ . For modules over commutative rings, $Soc (M) \subseteq Red (M)$ . By drawing motivation from how…