Combinatorial Interactions: Partition of Integers, Permutation Groups, and Nilpotent Orbits of Type A

Abstract

Partition of integers has various and extensive applications in divers area of Mathematics such as Combinatorics, Representation theories and Algebraic geometry. In this paper we gives an expository remark on some notable combinatorial interactions between partition of integers, group of permutations  and nilpotent orbits of type A. (where the underlying group defines the type and here the underlying group is the general linear group). Some of the results include counting of nilpotent orbits in type A, the cycle structure of elements of group of permutations S_n and enumeration of irreducible  module.