Fixed elements of pircon automorphisms

2023/07/05 by Hansson, Mikael, Umutabazi, Vincent
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.02473

Abstract

We prove that the subposet induced by the fixed elements of any automorphism of a pircon is also a pircon. By a result of Abdallah, Hansson, and Hultman, the order complex of any open interval in a pircon is a PL ball or a PL sphere. We apply our main results to symmetric groups of the form S_2n. A consequence is that the fixed point free signed involutions form a pircon under the dual of the Bruhat order on the hyperoctahedral group. Finally, we prove that this poset is, in fact, EL-shellable, which is a type B analogue of a result of Can, Cherniavsky, and Twelbeck.

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