Derivation of Cycle Index Formulas for Dihedral Group Acting on Unordered Triples
Journal: International Journal of Science and Research (IJSR) (Vol.6, No. 6)Publication Date: 2017-06-05
Authors : Geoffrey Muthoka;
Page : 32-35
Keywords : Cycle index; Cycle type; Monomial;
Abstract
The cycle index of dihedral group D_n acting on the set X of the vertices of a regular n-gon was studied by Harary and Palmer in 1973 (See [1]). In this paper we derive the cycle index formulas of the dihedral group (D_n) acting on unordered triples from the set X={1, 2, , n}. 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.
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