arXiv subjects

David Brewster

Publications and source records attributed to David Brewster.

2 recordsLinked to original sources

arXiv2021

Proper elements of Coxeter groups

We extend the notion of proper elements to all Coxeter groups. For all infinite families of finite Coxeter groups we prove that the probability a random element is proper goes to zero in the limit. This proves a conjecture of the third author and A. Yong regarding the proportion of Schubert varieties that are Levi spherical for all infinite families of Weyl groups. We also enumerate the proper elements in the exceptional Coxeter groups.

math.CO↗

arXiv2020

Proper permutations, Schubert geometry, and randomness

We define and study proper permutations. Properness is a geometrically natural necessary criterion for a Schubert variety to be Levi-spherical. We prove the probability that a random permutation is proper goes to zero in the limit.

math.CO↗