Enumeration of self-dual configurations

Edgar Milan Palmer and Robert William Robinson

Vol. 110 (1984), No. 1, 203–221

DOI: 10.2140/pjm.1984.110.203

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.

Mathematical Subject Classification 2000

Primary: 05C30

Secondary: 05A15, 05C15, 06E30, 20B25

Milestones

Received: 23 September 1981

Published: 1 January 1984