Séminaire Lotharingien de Combinatoire, 80B.64 (2018), 12 pp.
Nancy Abdallah, Mikael Hansson, and Axel Hultman
Topology of Posets with Special Partial Matchings
Abstract.
Special partial matchings (SPMs) are a generalisation of Brenti's
special matchings. Let a \emph{pircon} be a poset in which every
non-trivial principal order ideal is finite and admits an SPM. Thus
pircons generalise Marietti's zircons. We prove that every open
interval in a pircon is a PL ball or a PL sphere. It is then
demonstrated that Bruhat orders on certain twisted identities and
quasiparabolic W-sets constitute pircons. Together, these results
extend a result of Can, Cherniavsky, and Twelbeck, prove a conjecture
of Hultman, and confirm a claim of Rains and Vazirani.
Received: November 14, 2017.
Accepted: February 17, 2018.
Final version: April 1, 2018.
The following versions are available: