Reduced cycle indices and their applications in enumeration of NMR signals and equivalence classes

An efficient technique is formulated based on a polynomial structure which we call the reduced cycle index for the enumeration of equivalence classes and NMR signals under group action. The reduced cycle indices are shown to be the cycle index polynomials of a subset of significantly smaller order of the point group of the molecule. Thus, the reduced cycle indices are much simpler and their use leads to a considerable reduction in tile computation of the generating functions from the cycle indices and irreducible representations contained in a set.Alfred P. Sloan Fellow; Camille and Henry Dreyfus Teacher-Scholar.