Abstract
Let \(J_{n}^{B}\) denote the set of all fixed-point free involutions of the hyperoctahedral group \(B_{n}\), and let \(\hbox {des}_{B}(\pi )\) denote the number of descents of the permutation \(\pi \in B_{n}\). We show that \(J_{n}^{B}(t):=\sum _{\pi \in J_{n}^{B}}t^{\text {des}_{B}(\pi )}\) is symmetric, unimodal and \(\gamma \)-positive for \(n\ge 2\).
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Acknowledgements
This work was supported partially by the National Natural Science Foundation of China (No. 11871304), by the Young Talents Invitation Program of Shandong Province and by the Taishan Scholar Project of Shandong Province (No. tsqn202103060).
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Cao, J., Liu, L.L. The Eulerian distribution on the fixed-point free involutions of the hyperoctahedral group. J Algebr Comb 57, 793–810 (2023). https://doi.org/10.1007/s10801-022-01195-2
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DOI: https://doi.org/10.1007/s10801-022-01195-2