Classifications of rearrangement mechanisms by means of double cosets and counting formulas for the numbers of classes

Rearrangements of ligands attached at given sites of a certain skeleton may be classified according to two principles: symmetry equivalence, where the same permutation of objects is related to symmetry equivalent sites and rotational equivalence, where the resulting isomers differ just by their orientation. The combination of both these principles leads to a classification wanted by experimentalists. This latter classification is shown to be...