The cyclic sieving phenomenon

摘要

The cyclic sieving phenomenon is defined for generating functions of a set affording a cyclic group action, generalizing Stembridge's q = -1 phenomenon. The phenomenon is shown to appear in various situations, involving q-binomial coefficients, Polya-Redfield theory, polygon dissections, noncrossing partitions, finite reflection groups, and some finite field q-analogues. (C) 2004 Elsevier Inc. All rights reserved.