Thresholds for patterns in random compositions and random permutations

Thesis

Download PDF

Creator

Rights statement

Awarding institution

Date of award

Thesis identifier

Person Identifier (Local)

Qualification Level

Qualification Name

Department, School or Faculty

Abstract

We explore how the asymptotic structure of a random permutation of [n] with m inversions evolves, as m increases, establishing thresholds for the appearance and disappearance of any classical, consecutive or vincular pattern. Our investigation begins with exploring how the asymptotic structure of a random n-term weak integer composition of m evolves, as m increases from zero. The primary focus of our investigation into compositions is establishing thresholds for the appearance and disappearance of substructures, particularly the appearance and disappearance of consecutive composition patterns. We are then able to transfer the established composition threshold to establish the thresholds for classical, consecutive or vincular permutation patterns occurring within our random permutation model. This thesis is based on the papers [12] and [13].

Advisor / supervisor