The Eulerian distribution on the involutions of the hyperoctahedral group is unimodal

TL;DR

This paper proves that the Eulerian distribution on involutions of the hyperoctahedral group is unimodal, extending known results from the symmetric group, and provides its generating function using signed quasisymmetric functions.

Contribution

It establishes the unimodality of the Eulerian distribution for hyperoctahedral involutions and derives its generating function via signed quasisymmetric functions.

Findings

Eulerian distribution on hyperoctahedral involutions is unimodal

Generated explicit formula for the distribution's generating function

Extended unimodality results from symmetric to hyperoctahedral groups

Abstract

The Eulerian distribution on the involutions of the symmetric group is unimodal, as shown by Guo and Zeng. In this paper we prove that the Eulerian distribution on the involutions of the hyperoctahedral group, when viewed as a colored permutation group, is unimodal in a similar way and we compute its generating function, using signed quasisymmetric functions.