Notes on counting : an introduction to enumerative combinatorics / Peter J. Cameron (University of St Andrews, Scotland).

Author
Cameron, Peter J. (Peter Jephson), 1947- [Browse]
Format
Book
Language
English
Published/​Created
  • Cambridge, United Kingdom ; New York, NY, USA : Cambridge University Press, 2017.
  • ©2017
Description
xii, 222 pages : illustrations ; 24 cm.

Availability

Copies in the Library

Location Call Number Status Location Service Notes
Lewis Library - Stacks QA164 .C36 2017 Browse related items Request

    Details

    Subject(s)
    Series
    • Australian Mathematical Society lecture series ; 26. [More in this series]
    • Australian Mathematical Society Lecture Series ; 26
    Summary note
    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.
    Bibliographic references
    Includes bibliographical references (pages 212-216) and index.
    Contents
    • Introduction
    • Formal power series
    • Subsets, partitions, and permutations
    • recurrence relations
    • The permanent
    • q-analogues
    • Group actions and the cycle index
    • Mobius inversion
    • The Tutte polynomial
    • Species
    • Analytical methods: a first look
    • Further topics
    • Bibliography and further directions.
    ISBN
    • 9781108417365 (hardcover)
    • 1108417361 (hardcover)
    • 9781108404952 (paperback)
    • 1108404952 (paperback)
    OCLC
    983186719
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