AUNU POLYNOMIALS: EXCEDANCE NUMBER IN AUNU PERMUTATION/ INVOLUTIONS

Abstract

Abstract

An Involution is a Permutation which is equal to its own inverse. An involution is a permutation of a non-empty set which does not contain any permutation cycles of length greater than two  (i.e., it consists exclusively of fixed points and transpositions). In this research we obtain a generating function for the Aunu polynomials. The Aunu polynomials enumerate Aunu-permutation/Involutions according to their number of descents or their number of excedances. In this research we generated Aunu polynomials of orders: , however further investigation in the same pattern  would lead to generation of more polynomials of higher orders.

Keywords: Aunu-permutations, Involutions and permutation statistics.