Isomer counting and isomer permutation representation

A simple and safe approach for counting addition isomers or substitution isomers is described. This approach uses the concept of the isomer permutation representation.We obtain the isomer permutation representation directly by computing its characters, for which analytical formulae are presented. The approach is applied to benzene, cubane and three fullerene cages, D2-C76, D2-C84 and D2d-C84.