Cycle Index Formulas for Dn Acting on Ordered Pairs

Abstract

(2015) [2] studied the cycle index formula of the dihedral group acting on unordered pairs from the set -the n vertices of a regular -gon. In this paper we study the cycle index formulas of acting on ordered pairs from the set . In each case the actions of the cyclic part and the reflection part are studied separately for both an even value of and an odd value of .