Derivation of Cycle Index Formulas for Dihedral Group Acting on Unordered Triples

Geoffrey Muthoka

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.

Keywords: Cycle index, Cycle type, Monomial

How to Cite?: Geoffrey Muthoka, "Derivation of Cycle Index Formulas for Dihedral Group Acting on Unordered Triples", Volume 6 Issue 6, June 2017, International Journal of Science and Research (IJSR), Pages: 32-35, https://www.ijsr.net/getabstract.php?paperid=ART20173671, DOI: https://dx.doi.org/10.21275/ART20173671