Cyclic sieving is a well-known phenomenon where certain interesting
polynomials, especially q-analogues, have useful interpretations related to
actions and representations of the cyclic group. We propose a definition of
sieving for an arbitrary group G and study it for the dihedral group I2​(n)
of order 2n. This requires understanding the generators of the representation
ring of the dihedral group. For n odd, we exhibit several instances of
dihedral sieving which involve the generalized Fibonomial coefficients,
recently studied by Amdeberhan, Chen, Moll, and Sagan. We also exhibit an
instance of dihedral sieving involving Garsia and Haiman's (q,t)-Catalan
numbers.Comment: 10 page