Studies in the configuration interaction method. I. Combinatorial aspects of the downward-robb algorithm

The Downward‐Robb algorithm is one of the effective methods used in the unitary group approach to the configuration interaction treatment. The number of configurations corresponding to a given harmonic level (Paldus) or to a given total orbital weight (Downward‐Robb) can be determined by this algorithm. The knowledge of these numbers is essential for an effective implementation of the procedure. This article presents a new way to calculate these numbers. This procedure also yields novel relations among different partition functions.