On the combinatorics of crystal structures. II. Number of Wyckoff sequences of a given subdivision complexity.

Wyckoff sequences are a way of encoding combinatorial information about crystal structures of a given symmetry. In particular, they offer an easy access to the calculation of a crystal structure's combinatorial, coordinational and configurational complexity, taking into account the individual multiplicities (combinatorial degrees of freedom) and arities (coordinational degrees of freedom) associated with each Wyckoff position. However, distinct Wyckoff sequences can yield the same total numbers of combinatorial and coordinational degrees of freedom.