Automorphisms of the generalized cluster complex

Abstract

We exhibit a dihedral symmetry in the generalized cluster complex defined by Fomin and Reading. Together with diagram symmetries, they generate the automorphism group of the complex. A consequence is a simple explicit formula for the order of this automorphism group.

Keywords

• Cluster complex
• Finite Coxeter group
• Automorphism group
• Dihedral group
• Symmetry