Refined Catalan and Narayana cyclic sieving

Abstract

We prove several new instances of the cyclic sieving phenomenon (CSP) on Catalan objects of type A and type B. Moreover, we refine many of the known instances of the CSP on Catalan objects. For example, we consider triangulations refined by the number of "ears", non-crossing matchings with a fixed number of short edges, and non-crossing configurations with a fixed number of loops and edges.

Updated version, minor changes

References in corpus (5)

• Cyclic Descents for General Skew Tableaux
• Skew characters and cyclic sieving
• The Cone of Cyclic Sieving Phenomena
• $q$-dimensions of highest weight crystals and cyclic sieving phenomenon
• Counting orbits under Kreweras complementation