Cycle Index Formulas for Dihedral Group (DDnn) Acting On Ordered Triples

Abstract

The cycle index of dihedral group DDnn acting on the set XX of the vertices of a regular nn-gon was studied by Harary and Palmer in 1973 (See [1]). In this paper we study the cycle index formulas of DDnn acting on unordered triples from the set XX = {1,2, ... , nn}. In each case the actions of the cyclic part and the reflection part are studied separately for both an even value of nn and an odd value of nn.