Generalised inversion frequency distribution

Abstract

The thesis is a study of the distribution of inversion counts for the permutations of multisets by a four-tier architecture of integers, partitions, multisets, and the permutations of the multisets. It introduces two insertion methods to link the hierarchical and peer to peer relationships between these entities. It centers around the generating function for the inversion count distribution for the permutation of the multisets. The main result is a recursive function for the parent/child relationship between the permutations of multisets. The thesis also studies the link between the coefficients of the generating polynomial and the Ferrers diagram and also delivers an integer partition formula as a special case of the closed-form. It also analyses the conformance of natural and computer-generated sequences with the expected distribution of partition and inversion counts