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

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