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Notes on counting : an introduction to enumerative combinatorics / Peter J. Cameron (University of St Andrews, Scotland).
Author
Cameron, Peter J. (Peter Jephson), 1947-
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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
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Details
Subject(s)
Combinatorial analysis
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Mathematical analysis
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Numeration
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Series
Australian Mathematical Society lecture series ; 26.
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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.
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ISBN
9781108417365 (hardcover)
1108417361 (hardcover)
9781108404952 (paperback)
1108404952 (paperback)
OCLC
983186719
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