Refined Catalan and Narayana cyclic sieving

• 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.

Subject headings

NATURVETENSKAP  -- Matematik -- Diskret matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Discrete Mathematics (hsv//eng)

Keyword

Dyck paths

cyclic sieving

Narayana numbers

major index

q-analog

Publication and Content Type

ref (subject category)

art (subject category)