Merris Combinatorics

2. Auflage 2003
ISBN: 978-0-471-45849-4
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 576 Seiten, E-Book

Reihe: Wiley-Interscience Series in Discrete Mathematics and Optimization

A mathematical gem-freshly cleaned and polished
This book is intended to be used as the text for a first coursein combinatorics. the text has been shaped by two goals, namely, tomake complex mathematics accessible to students with a wide rangeof abilities, interests, and motivations; and to create apedagogical tool, useful to the broad spectrum of instructors whobring a variety of perspectives and expectations to such acourse.
Features retained from the first edition:
* Lively and engaging writing style
* Timely and appropriate examples
* Numerous well-chosen exercises
* Flexible modular format
* Optional sections and appendices
Highlights of Second Edition enhancements:
* Smoothed and polished exposition, with a sharpened focus on keyideas
* Expanded discussion of linear codes
* New optional section on algorithms
* Greatly expanded hints and answers section
* Many new exercises and examples

Autoren/Hrsg.

Merris, Russell

Inhaltsverzeichnis

Preface.
Chapter 1: The Mathematics of Choice.
1.1. The Fundamental Counting Principle.
1.2. Pascal's Triangle.
*1.3. Elementary Probability.
*1.4. Error-Correcting Codes.
1.5. Combinatorial Identities.
1.6. Four Ways to Choose.
1.7. The Binomial and Multinomial Theorems.
1.8. Partitions.
1.9. Elementary Symmetric Functions.
*1.10. Combinatorial Algorithms.
Chapter 2: The Combinatorics of Finite Functions.
2.1. Stirling Numbers of the Second Kind.
2.2. Bells, Balls, and Urns.
2.3. The Principle of Inclusion and Exclusion.
2.4. Disjoint Cycles.
2.5. Stirling Numbers of the First Kind.
Chapter 3: Pólya's Theory of Enumeration.
3.1. Function Composition.
3.2. Permutation Groups.
3.3. Burnside's Lemma.
3.4. Symmetry Groups.
3.5. Color Patterns.
3.6. Pólya's Theorem.
3.7. The Cycle Index Polynomial.
Chapter 4: Generating Functions.
4.1. Difference Sequences.
4.2. Ordinary Generating Functions.
4.3. Applications of Generating Functions.
4.4. Exponential Generating Functions.
4.5. Recursive Techniques.
Chapter 5: Enumeration in Graphs.
5.1. The Pigeonhole Principle.
*5.2. Edge Colorings and Ramsey Theory.
5.3. Chromatic Polynomials.
*5.4. Planar Graphs.
5.5. Matching Polynomials.
5.6. Oriented Graphs.
5.7. Graphic Partitions.
Chapter 6: Codes and Designs.
6.1. Linear Codes.
6.2. Decoding Algorithms.
6.3. Latin Squares.
6.4. Balanced Incomplete Block Designs.
Appendix A1: Symmetric Polynomials.
Appendix A2: Sorting Algorithms.
Appendix A3: Matrix Theory.
Bibliography.
Hints and Answers to Selected Odd-Numbered Exercises.
Index of Notation.
Index.
Note: Asterisks indicate optional sections that can be omittedwithout loss of continuity.

Über Autor(innen)

RUSSELL MERRIS, PhD, is Professor of Mathematics and Computer Science at California State University, Hayward. Among his other books is Graph Theory, also published by Wiley.