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Séminaire Lotharingien de Combinatoire, B69b (2013), 20 pp.

# Jang Soo Kim

# Cyclic Sieving Phenomena on Annular Noncrossing Permutations

**Abstract.**
We show cyclic sieving phenomena on annular noncrossing permutations with
given cycle types. We define annular *q*-Kreweras numbers, annular
*q*-Narayana numbers, and annular *q*-Catalan numbers, and show that a sum of
annular *q*-Kreweras numbers becomes an annular *q*-Narayana number and a sum
of annular *q*-Narayana numbers becomes an annular *q*-Catalan number. We also
show that these polynomials are closely related to the cyclic sieving
phenomena on annular noncrossing permutations.

Received: November 7, 2012.
Revised: February 22, 2013.
Accepted: March 29, 2013.

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