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TOPICS IN COMBINATORICS

Module code: MT544V
Credits: 10
Semester: 2
Department: MATHEMATICS AND STATISTICS
International:

	Overview
	Various combinatorial structures such as strongly regular graphs, designs, codes and orthogonal arrays. Connections between these objects and algebraic techniques associated with their analysis. Introduction: designs, graphs, codes, orthogonal arrays, examples & constructions Strongly Regular Graphs: adjacency matrices, parameters, existence criteria, Cayley graphs, partial difference sets Codes: parameters, bounds, two-weight codes, weight enumerators Designs: examples, incidence matrices, parameters, existence criteria, codes & designs Orthogonal Arrays: constructions, bounds, codes & arrays

Overview

Various combinatorial structures such as strongly regular graphs, designs, codes and orthogonal arrays. Connections between these objects and algebraic techniques associated with their analysis.

Introduction: designs, graphs, codes, orthogonal arrays, examples & constructions
Strongly Regular Graphs: adjacency matrices, parameters, existence criteria, Cayley graphs, partial difference sets
Codes: parameters, bounds, two-weight codes, weight enumerators
Designs: examples, incidence matrices, parameters, existence criteria, codes & designs
Orthogonal Arrays: constructions, bounds, codes & arrays

	Learning Outcomes
	On successful completion of the module, students should be able to: State some of the classical theorems of combinatorics. Prove any of the theorems given in the course. Deduce properties which follow from these theorems. Prove other combinatorial results using rigorous arguments.

Teaching & Learning methods

Assessment

	Autumn Supplementals/Resits
	No autumn repeat.

	Pre-Requisites
	Familiarity with groups, rings, finite fields, linear algebra

	Additional Reading
	Texts: A Course in Combinatorics, J.H. van Lint & R.M. Wilson, C.U.P. Designs, Codes, Graphs and Their Links, P.J. Cameron, J.H. van Lint, C.U.P. Orthogonal Arrays, A.S. Hedayat, N.J.A. Sloane, J. Stufken, Springer

	Timetable
	This timetable is not currently available, please contact the Mathematics And Statistics Department.

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Courses / Module

TOPICS IN COMBINATORICS