How to count : an introduction to combinatorics / R.B.J.T. Allenby, Alan Slomson.

By:

Allenby, R. B. J. T

Contributor(s):

Slomson, Alan

Material type: Text

TextSeries: Discrete mathematics and its applicationsPublication details: Boca Raton, FL. : CRC Press, 2011.Edition: 2. edDescription: xv, 430p. : ill. ; 27 cmISBN:

9781420082609 (hardback)
1420082604 (hardback)

Subject(s):

Combinatorial analysis

Holdings
Item type	Current library	Call number	Copy number	Status	Date due	Barcode
Standard Loan	Thurles Library Main Collection	511.6 ALL (Browse shelf(Opens below))	1	Available		39002100501585
Standard Loan	Thurles Library Main Collection	511.6 ALL (Browse shelf(Opens below))	2	Available		39002100501593

Enhanced descriptions from Syndetics:

Emphasizes a Problem Solving Approach
A first course in combinatorics

Completely revised, How to Count: An Introduction to Combinatorics, Second Edition shows how to solve numerous classic and other interesting combinatorial problems. The authors take an easily accessible approach that introduces problems before leading into the theory involved. Although the authors present most of the topics through concrete problems, they also emphasize the importance of proofs in mathematics.

New to the Second Edition
This second edition incorporates 50 percent more material. It includes seven new chapters that cover occupancy problems, Stirling and Catalan numbers, graph theory, trees, Dirichlet's pigeonhole principle, Ramsey theory, and rook polynomials. This edition also contains more than 450 exercises.

Ideal for both classroom teaching and self-study, this text requires only a modest amount of mathematical background. In an engaging way, it covers many combinatorial tools, such as the inclusion-exclusion principle, generating functions, recurrence relations, and Pólya's counting theorem.

Includes bibliographical references and index.

First published as: an introduction to combinatorics, 1991.

Table of contents provided by Syndetics

Preface to the Second Edition (p. xi)
Acknowledgments (p. xiii)
Authors (p. xv)
Chapter 1 What's it All About? (p. 1)
1.1 What is Combinatorics? (p. 1)
1.2 Classic Problems (p. 2)
1.3 What You Need to Know (p. 14)
1.4 Are you Sitting Comfortably? (p. 15)
Chapter 2 Permutations and Combinations (p. 17)
2.1 The Combinatorial Approach (p. 17)
2.2 Permutations (p. 17)
2.3 Combinations (p. 21)
2.4 Applications to Probability Problems (p. 28)
2.5 The Multinomial Theorem (p. 34)
2.6 Permutations and Cycles (p. 36)
Chapter 3 Occupancy Problems (p. 39)
3.1 Counting the Solutions of Equations (p. 39)
3.2 New Problems from Old (p. 43)
3.3 A "Reduction" Theorem for the Stirling Numbers (p. 47)
Chapter 4 The Inclusion-Exclusion Principle (p. 51)
4.1 Double Counting (p. 51)
4.2 Derangements (p. 58)
4.3 A Formula for the Stirling Numbers (p. 60)
Chapter 5 Stirling and Catalan Numbers (p. 63)
5.1 Stirling Numbers (p. 63)
5.2 Permutations and Stirling Numbers (p. 68)
5.3 Catalan Numbers (p. 71)
Chapter 6 Partitions and Dot Diagrams (p. 81)
6.1 Partitions (p. 81)
6.2 Dot Diagrams (p. 83)
6.3 A Bit of Speculation (p. 89)
6.4 More Proofs Using Dot Diagrams (p. 92)
Chapter 7 Generating Functions and Recurrence Relations (p. 95)
7.1 Functions and Power Series (p. 95)
7.2 Generating Functions (p. 98)
7.3 What is a Recurrence Relation? (p. 101)
7.4 Fibonacci Numbers (p. 103)
7.5 Solving Homogeneous Linear Recurrence Relations (p. 109)
7.6 Nonhomogeneous Linear Recurrence Relations (p. 114)
7.7 The Theory of Linear Recurrence Relations (p. 120)
7.8 Some Nonlinear Recurrence Relations (p. 124)
Chapter 8 Partitions and Generating Functions (p. 127)
8.1 The Generating Function for the Partition Numbers (p. 127)
8.2 A Quick(ish) Way of Finding p(n) (p. 132)
8.3 An Upper Bound for the Partition Numbers (p. 142)
8.4 The Hardy-Ramanujan Formula (p. 145)
8.5 The Story of Hardy and Ramanujan (p. 147)
Chapter 9 Introduction to Graphs (p. 151)
9.1 Graphs and Pictures (p. 151)
9.2 Graphs: A Picture-Free Definition (p. 152)
9.3 Isomorphism of Graphs (p. 154)
9.4 Paths and Connected Graphs (p. 163)
9.5 Planar Graphs (p. 168)
9.6 Eulerian Graphs (p. 178)
9.7 Hamiltonian Graphs (p. 182)
9.8 The Four-Color Theorem (p. 188)
Chapter 10 Trees (p. 199)
10.1 What is a Tree? (p. 199)
10.2 Labeled Trees (p. 204)
10.3 Spanning Trees and Minimal Connectors (p. 210)
10.4 The Shortest-Path Problem (p. 217)
Chapter 11 Groups of Permutations (p. 223)
11.1 Permutations as Groups (p. 223)
11.2 Symmetry Groups (p. 229)
11.3 Subgroups and Lagrange's Theorem (p. 235)
11.4 Orders of Group Elements (p. 240)
11.5 The Orders of Permutations (p. 242)
Chapter 12 Group Actions (p. 245)
12.1 Colorings (p. 245)
12.2 The Axioms for Group Actions (p. 247)
12.3 Orbits (p. 249)
12.4 Stabilizers (p. 250)
Chapter 13 Counting Patterns (p. 257)
13.1 Frobenius's Counting Theorem (p. 257)
13.2 Applications of Frobenius's Counting Theorem (p. 259)
Chapter 14 Pólya Counting (p. 267)
14.1 Colorings and Group Actions (p. 267)
14.2 Pattern Inventories (p. 270)
14.3 The Cycle Index of a Group (p. 274)
14.4 Pólya's Counting Theorem: Statement and Examples (p. 277)
14.5 Pólya's Counting Theorem: The Proof (p. 281)
14.6 Counting Simple Graphs (p. 285)
Chapter 15 Dirichlet's Pigeonhole Principle (p. 293)
15.1 The Origin of the Principle (p. 293)
15.2 The Pigeonhole Principle (p. 294)
15.3 More Applications of the Pigeonhole Principle (p. 297)
Chapter 16 Ramsey Theory (p. 303)
16.1 What is Ramsey's Theorem? (p. 303)
16.2 Three Lovely Theorems (p. 310)
16.3 Graphs of Many Colors (p. 314)
16.4 Euclidean Ramsey Theory (p. 315)
Chapter 17 Rook Polynomials and Matchings (p. 319)
17.1 How Rook Polynomials are Defined (p. 319)
17.2 Matchings and Marriages (p. 332)
Solutions to the A Exercises (p. 339)
Books for Further Reading (p. 419)
Index for Notation (p. 421)
Index (p. 423)

Author notes provided by Syndetics

Alan Slomson taught mathematics at the University of Leeds from 1967 to 2008. He is currently the secretary of the United Kingdom Mathematics Trust.

R.B.J.T. Allenby taught mathematics at the University of Leeds from 1965 to 2007.