An Inversion Statistic on the Hyperoctahedral Group

2023/07/11 by Arslan, Hasan, Altoum, Alnour, Arslan, Hilal Karakus
#05A05 #05A15 #05A19 #20F55 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.05198

Abstract

In this paper, we introduce an inversion statistic on the hyperoctahedral group B_n 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 B_n 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 flag-major index is equi-distributed with this inversion statistic on B_n.

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