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Introductory Combinatorics

by: Brualdi, Richard A.

Introductory Combinatorics

by: Brualdi, Richard A.

ISBN 13:
9780131814882
ISBN 10:
0131814885
Edition: 3rd
Format: Hardcover
Copyright: 01/01/1999
Publisher: Pearson College Div

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Summary

Appropriate for an undergraduate junior/senior level mathematics course on combinatorics. This book emphasizes combinatorial ideas including the pigeon-hole principle, counting techniques, permutations and combinations, Polya counting, binomial coefficients, inclusion-exclusion principle, generating functions and recurrence relations, and combinatortial structures (matchings, designs, graphs).

Preface

Chapter 1. What is Combinatorics?

(26)

1.1 Example. Perfect covers of chessboards

(4)

1.2 Example. Cutting a cube

(2)

1.3 Example. Magic squares

(3)

1.4 Example. The 4-color problem

(1)

1.5 Example. The problem of the 36 officers

(2)

1.6 Example. Shortest-route problem

(2)

1.7 Example. The game of Nim

(3)

1.8 Exercises

(6)

Chapter 2. The Pigeonhole Principle

(18)

2.1 Pigeonhole principle: Simple form

(5)

2.2 Pigeonhole principle: Strong form

(4)

2.3 A theorem of Ramsey

(5)

2.4 Exercises

(4)

Chapter 3. Permutations and Combinations

(36)

3.1 Two basic counting principles

(8)

3.2 Permutations of sets

(7)

3.3 Combinations of sets

(4)

3.4 Permutations of multisets

(6)

3.5 Combinations of multisets

(5)

3.6 Exercises

(6)

Chapter 4. Generating Permutations and Combinations

(41)

4.1 Generating permutations

(6)

4.2 Inversions in permutations

(6)

4.3 Generating combinations

(16)

4.5 Partial orders and equivalence relations

109

(7)

4.6 Exercises

116

(6)

Chapter 5. The Binomial Coefficients

122

(37)

5.1 Pascal's formula

122

(5)

5.2 The binomial theorem

127

(3)

5.3 Identities

130

(7)

5.4 Unimodality of binomial coefficients

137

(6)

5.5 The multinomial theorem

143

(4)

5.6 Newton's binomial theorem

147

(2)

5.7 More on partially ordered sets

149

(3)

5.8 Exercises

152

(7)

Chapter 6. The Inclusion-Exclusion Principle and Applications

159

(31)

6.1 The inclusion-exclusion principle

159

(9)

6.2 Combinations with repetition

168

(4)

6.3 Derangements

172

(6)

6.4 Permutations with forbidden positions

178

(5)

6.5 Another forbidden position problem

183

(2)

6.6 Exercises

185

(5)

Chapter 7. Recurrence Relations and Generating Functions

190

(62)

7.1 Some number sequences

191

(11)

7.2 Linear homogeneous recurrence relations

202

(11)

7.3 Non-homogeneous recurrence relations

213

(7)

7.4 Generating functions

220

(7)

7.5 Recurrences and generating functions

227

(8)

7.6 A geometry example

235

(5)

7.7 Exponential generating functions

240

(6)

7.8 Exercises

246

(6)

Chapter 8. Special Counting Sequences

252

(42)

8.1 Catalan numbers

252

(9)

8.2 Difference sequences and Stirling numbers

261

(20)

8.3 Partition numbers

281

(4)

8.4 A geometric problem

285

(5)

8.5 Exercises

290

(4)

Chapter 9. Matchings in Bipartite Graphs

294

(43)

9.1 General problem formulation

295

(7)

9.2 Matchings

302

(17)

9.3 Systems of distinct representatives

319

(5)

9.4 Stable marriages

324

(8)

9.5 Exercises

332

(5)

Chapter 10. Combinatorial Designs

337

(63)

10.1 Modular arithmetic

337

(13)

10.2 Block designs

350

(12)

10.3 Steiner triple systems

362

(7)

10.4 Latin squares

369

(24)

10.5 Exercises

393

(7)

Chapter 11. Introduction to Graph Theory

400

(75)

11.1 Basic properties

401

(11)

11.2 Eulerian trails

412

(10)

11.3 Hamilton chains and cycles

422

(7)

11.4 Bipartite multigraphs

429

(7)

11.5 Trees

436

(7)

11.6 The Shannon switching game

443

(7)

11.7 More on trees

450

(13)

11.8 Exercises

463

(12)

Chapter 12. Digraphs and Networks

475

(26)

12.1 Digraphs

475

(13)

12.2 Networks

488

(8)

12.3 Exercises

496

(5)

Chapter 13. More on Graph Theory

501

(45)

13.1 Chromatic number

502

(12)

13.2 Plane and planar graphs

514

(5)

13.3 A 5-color theorem

519

(4)

13.4 Independence number and clique number

523

(10)

13.5 Connectivity

533

(7)

13.6 Exercises

540

(6)

Chapter 14. Polya Counting

546

(46)

14.1 Permutation and symmetry groups

547

(12)

14.2 Burnside's theorem

559

(7)

14.3 Polya's counting formula

566

(20)

14.4 Exercises

586

(6)

Answers and Hints to Exercises

592

(15)

Bibliography

607

(2)

Index

609

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Introductory Combinatorics

Introductory Combinatorics

9780131814882

0131814885

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Introductory Combinatorics

Introductory Combinatorics

9780131814882

0131814885

Summary

Table of Contents

Supplemental Materials

Write a Review

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