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Refined Catalan and Narayana cyclic sieving

  • Author(s): Alexandersson, Per;
  • Linusson, Svante;
  • Potka, Samu;
  • Uhlin, Joakim
  • et al.

Published Web Location Commons 'BY' version 4.0 license

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.

Keywords: Dyck paths, cyclic sieving, Narayana numbers, major index, q-analog.

Mathematics Subject Classifications: 05E18, 05A19, 05A30

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