Abstract. Cyclic sieving is a well-known phenomenon where certain interesting polynomials, especially qanalogues, have useful interpretations related to actions and representations of the cyclic group. We define sieving for an arbitrary group G and study it for the dihedral group I2pnq of order 2n. This requires understanding the generators of the representation ring of the dihedral group. For ...

We consider the dihedral model of motion for chains with fixed edge lengths, in which the angle between every pair of successive edges remains fixed. A chain is flat-state connected if every planar configuration can be transformed to any other via a series of dihedral motions which maintain simplicity. Here we prove that three classes of chains are flat-state connected. The first class is that ...