Peter J. Cameron

Notes on Counting: An Introduction to Enumerative Combinatorics (eBook, PDF)

• Format: PDF

Produktbeschreibung

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-Polya theory of cycle indices, Mobius inversion, the Tutte polynomial, and species.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 21. Juni 2017
• Englisch
• ISBN-13: 9781108280884
• Artikelnr.: 52992731

Autorenporträt

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.

Inhaltsangabe

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.