Cycle Index Formulas for Dn Acting on Unordered Pairs

Abstract

The cycle index of dihedral group Dn acting on the set X of the vertices of a regular -gon was studied (See [1]). In this paper we study the cycle index formulas of Dn acting on unordered pairs from the set x . In each case the actions of the cyclic part and the reflection part are studied separately for both an even value of n and an odd value of n .