Enumeration of self-dual configurations

Abstract

A variety of combinatorial structures are self-dual in the sense that opposite elements have opposite properties. We provide a general enumeration theorem for these which has a number of interesting applications including the enumeration of self-dual boolean functions and 2-colorings of the vertices of polyhedra in which opposite vertices have different colors. Our method involves a modification of Pólya’s enumeration theorem. © 1984 by Pacific Journal of Mathematics.