On The Cycle Indices Of The Cyclic And Dihedral Groups Acting On The Cartesian Product Of X

ABSTRACT The concept of cycle index was first discovered by Howard Redfield in 1927. The cycle index formulas of various group actions have been computed since then by various authors. The formulas have been used to count graphs in mathematics and chemical compounds in chemistry. Therefore cycle index is a very useful tool in enumeration. It is widely applied in other fields of study like biology and jewelry industry. The cycle index of the symmetric group acting on ordered pairs, triples and on -ordered element subset has so far been done. The cycle index of dihedral and cyclic groups acting…