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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