Combinatorics

Russell Merris

568 pages, parution le 15/09/2003 (2^eme édition)

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Résumé

A mathematical gem-freshly cleaned and polished

This book is intended to be used as the text for a first course in combinatorics. the text has been shaped by two goals, namely, to make complex mathematics accessible to students with a wide range of abilities, interests, and motivations; and to create a pedagogical tool, useful to the broad spectrum of instructors who bring a variety of perspectives and expectations to such a course.

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 key ideas
Expanded discussion of linear codes
New optional section on algorithms
Greatly expanded hints and answers section
Many new exercises and examples

The Mathematics of Choice
- The Fundamental Counting Principle
- Pascal's Triangle
- Elementary Probability
- Error-Correcting Codes
- Combinatorial Identities
- Four Ways to Choose
- The Binomial and Multinomial Theorems
- Partitions
- Elementary Symmetric Functions
- Combinatorial Algorithms
The Combinatorics of Finite Functions
- Stirling Numbers of the Second Kind
- Bells, Balls, and Urns
- The Principle of Inclusion and Exclusion
- Disjoint Cycles
- Stirling Numbers of the First Kind
Pólya's Theory of Enumeration
- Function Composition
- Permutation Groups
- Burnside's Lemma
- Symmetry Groups
- Color Patterns
- Pólya's Theorem
- The Cycle Index Polynomial
Generating Functions
- Difference Sequences
- Ordinary Generating Functions
- Applications of Generating Functions
- Exponential Generating Functions
- Recursive Techniques
Enumeration in Graphs
- The Pigeonhole Principle
- Edge Colorings and Ramsey Theory
- Chromatic Polynomials
- Planar Graphs
- Matching Polynomials
- Oriented Graphs
- Graphic Partitions
Codes and Designs
- Linear Codes
- Decoding Algorithms
- Latin Squares
- Balanced Incomplete Block Designs
Appendices
Bibliography
Hints and Answers to Selected Odd-Numbered Exercises
Index of Notation
Index

L'auteur - Russell Merris

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.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Wiley
Auteur(s)	Russell Merris
Parution	15/09/2003
Édition	2^eme édition
Nb. de pages	568
Format	16 x 24
Couverture	Relié
Poids	660g
Intérieur	Noir et Blanc
EAN13	9780471262961
ISBN13	978-0-471-26296-1