The Eulerian distribution on the fixed-point free involutions of the hyperoctahedral group

Let J n B denote the set of all fixed-point free involutions of the hyperoctahedral group B n , and let des B ( π ) denote the number of descents of the permutation π ∈ B n . We show that J n B ( t ) : = ∑ π ∈ J n B t des B ( π ) is symmetric, unimodal and γ -positive for n ≥ 2 .

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Bibliographic Details
Published in	Journal of algebraic combinatorics Vol. 57; no. 3; pp. 793 - 810
Main Authors	Cao, Jie, Liu, Lily Li
Format	Journal Article
Language	English
Published	New York Springer US 01.05.2023 Springer Nature B.V
Subjects	Combinatorics Computer Science Convex and Discrete Geometry Group theory Group Theory and Generalizations Lattices Mathematics Mathematics and Statistics Order Ordered Algebraic Structures Permutations Unimodality Involution positivity 05A20 05A05 05A15 Symmetry Hyperoctahedral group
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Summary:	Let J n B denote the set of all fixed-point free involutions of the hyperoctahedral group B n , and let des B ( π ) denote the number of descents of the permutation π ∈ B n . We show that J n B ( t ) : = ∑ π ∈ J n B t des B ( π ) is symmetric, unimodal and γ -positive for n ≥ 2 .
ISSN:	0925-9899 1572-9192
DOI:	10.1007/s10801-022-01195-2