Fixed points of zircon automorphisms

2007/03/16 by Axel Hultman, Hultman, Axel
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.math/0703482

5 pages

arxiv created 2007/03/16 · arxiv updated 2009/12/01

Abstract

A zircon is a poset in which every principal order ideal is finite and equipped with a so-called special matching. We prove that the subposet induced by the fixed points of any automorphism of a zircon is itself a zircon. This provides a natural context in which to view recent results on Bruhat orders on twisted involutions in Coxeter groups.

Related

• Fixed points of involutive automorphisms of the Bruhat order
• Topology of posets with special partial matchings
• Fixed elements of pircon automorphisms
• Zircons and smooth Bruhat intervals in symmetric groups
• Fixed points in compactifications and combinatorial counterparts