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.

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