Notes on Counting: An Introduction to Enumerative Combinatorics

An introduction to enumerative combinatorics, vital to many areas of mathematics. It is suitable as a class text or for individual study.

Peter J. Cameron (Author)

9781108404952, Cambridge University Press

Paperback / softback, published 21 June 2017

234 pages, 17 b/w illus. 140 exercises
22.7 x 15.2 x 1.3 cm, 0.35 kg

'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

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.

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.

Subject Areas: Combinatorics & graph theory [PBV], Discrete mathematics [PBD]