Counting Orbits

The purpose of this chaper is to introduce the Pólya-Redfield theorem, which has been widely used for enumeration of chemical compounds. This theorem is of fundamental importance, not only because of its wide applicability but also because of its conceptual depth.[1, 2] Many mathematical textbooks have dealt with the topics in various manners.[3]–[7] Chemical enumerations have been reviewed in several books[8]–[10] and articles.[11]–[13] Recent advances of chemical enumerations have been reported.[14] We have reported enumerations of organic reactions after the formulation of imaginary transition structures.[15]