Notes on Counting

An Introduction to Enumerative Combinatorics

Peter J. Cameron (University of St Andrews, Scotland)

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English

Cambridge University Press
29 June 2017

Discrete mathematics; Combinatorics & graph theory

Series: Australian Mathematical Society Lecture Series

Enumerative combinatorics, in its algebraic and analytic forms, is vital to many areas of mathematics, from model theory to statistical mechanics. This book, which stems from many years' experience of teaching, invites students into the subject and prepares them for more advanced texts. It is suitable as a class text or for individual study. The author provides proofs for many of the theorems to show the range of techniques available, and uses examples to link enumerative combinatorics to other areas of study. The main section of the book introduces the key tools of the subject (generating functions and recurrence relations), which are then used to study the most important combinatorial objects, namely subsets, partitions, and permutations of a set. Later chapters deal with more specialised topics, including permanents, SDRs, group actions and the Redfield–Pólya theory of cycle indices, Möbius inversion, the Tutte polynomial, and species.

By: Peter J. Cameron (University of St Andrews Scotland)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 26
Dimensions: Height: 235mm, Width: 156mm, Spine: 17mm
Weight: 460g
ISBN: 9781108417365
ISBN 10: 1108417361
Series: Australian Mathematical Society Lecture Series
Pages: 234
Publication Date: 29 June 2017
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

1. Introduction; 2. Formal power series; 3. Subsets, partitions and permutations; 4. Recurrence relations; 5. The permanent; 6. q-analogues; 7. Group actions and cycle index; 8. Mobius inversion; 9. The Tutte polynomial; 10. Species; 11. Analytic methods: a first look; 12. Further topics; 13. Bibliography and further directions; Index.

Peter J. Cameron is a Professor in the School of Mathematics and Statistics at the University of St Andrews, Scotland. Much of his work has centred on combinatorics and, since 1992, he has been Chair of the British Combinatorial Committee. He has also worked in group and semigroup theory, model theory, and other subjects such as statistical mechanics and measurement theory. Peter J. Cameron is the recipient of the Senior Whitehead Prize of 2017 from the London Mathematical Society.

Reviews for Notes on Counting: An Introduction to Enumerative Combinatorics

'It's indeed a very good introduction to enumerative combinatorics and has all the trappings of a pedagogically sound enterprise, in the old-fashioned sense: exercises, good explanations (not too terse, but certainly not too wordy), and mathematically serious (nothing namby-pamby here). It's an excellent book.' Michael Berg, MAA Reviews 'Cameron's Notes on Counting is a clever introductory book on enumerative combinatorics ... Overall, the text is well-written with a friendly tone and an aesthetic organization, and each chapter contains an ample number of quality exercises. Summing Up: Recommended.' A. Misseldine, CHOICE