Combinatorics

AY2022/2023 Semester 1

This final year mathematics course aims to equip you to apply concepts in symbolic methods and analysis to solve a variety of problems in combinatorics. The tools developed in the course are useful for future graduate courses in mathematics, applied mathematics and engineering. Course Content 1. Combinatorial Structures and Ordinary Generating Functions: symbolic enumeration methods, integer compositions and partitions, words and regular languages, tree structures 2. Labelled Structures and Exponential Generating Functions: labelled classes, surjections, set partitions, words, alignments, permutations, labelled trees, mapping and graphs 3. Complex Analysis, Rational and Meromorphic Asymptotics: generating functions as analytic objects, analytic functions and meromorphic functions, singularities and exponential growth of coefficients 4. Singularity Analysis of Generating Functions: coefficient asymptotics, process of singularity analysis