The cyclic sieving phenomenon 
V. Reiner, D. Stanton and D. E. White

ABSTRACT: 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 theory, polygon dissections, 
non-crossing partitions, finite reflection groups, and some finite field 
q-analogues.