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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