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The Eulerian Distribution on the Involutions of the Hyperoctahedral Group is Unimodal

  • Vassilis-Dionyssis MoustakasEmail author
Original Paper

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.

Keywords

Involution Descent Unimodality Hyperoctahedral group Quasisymmetric function 

Mathematics Subject Classification

05A15 05A20 05E05 

Notes

Acknowledgements

The author would like to thank Christos Athanasiadis for suggesting the problem of unimodality of \(I_{n}^{B}(x)\) and for valuable discussions.

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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.National and Kapodistrian University of AthensAthensGreece

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