ALGEBRAIC THEORIES OF AUNU PERMUTATION GROUPS WITH CARDINALITY 10, 12 and 14 USING GROUP ACTION

Abstract

Permutation groups have played important roles in method of enumerating combinatorial objects in recent times. However, the study of the applicability of AUNU permutation groups using group action is receiving less 
attention.  In this paper, a method of constructing an associative group action using the subsequences of (123) avoiding pattern of AUNU Permutation groups with Cardinality 10,12 and 14 is provided. The method used the 
generating function of AUNU groups in the construction to obtain some geometric structures of orbits resembling to lattice structure which led to the establishment of some algebraic theoretic consequences and. properties of 
group action such as in the orbit and stabilizer of permutation groups.