An Inversion Statistic on the Hyperoctahedral Group
Combinatorics
2023-07-21 v2
Abstract
In this paper, we introduce an inversion statistic on the hyperoctahedral group by using an decomposition of a positive root system of this reflection group. Then we prove some combinatorial properties for the inversion statistic. We establish an enumeration system on the group and give an efficient method to uniquely derive any group element known its enumeration order with the help of the inversion table. In addition, we prove that the \textit{flag-major index} is equi-distributed with this inversion statistic on .
Keywords
Cite
@article{arxiv.2307.05198,
title = {An Inversion Statistic on the Hyperoctahedral Group},
author = {Hasan Arslan and Alnour Altoum and Hilal Karakus Arslan},
journal= {arXiv preprint arXiv:2307.05198},
year = {2023}
}