Combinatorics Problems and Solutions, Second Edition

Stefan Hollos and J. Richard Hollos

Format and pricing: Paperback (217 pages) $19.95, pdf (217 pages) $12.95
ISBN: 9781887187480
Publication date: April 2024

This book will help you learn combinatorics in the most effective way possible - through problem solving. It contains 263 combinatorics problems with detailed solutions.

Combinatorics is the part of mathematics that involves counting. It is therefore an essential part of anyone's mathematical toolkit. The applications of combinatorics include probability, cryptography, error correcting, games, music and visual art.

In this new edition we have expanded the introductory section by more than twice the original size, and the number of problems has grown by over 30%. There are new sections on the pigeon hole principle and integer partitions with accompanying problems. Many of the new problems are application oriented. There are also new combinatorial geometry problems.

Someone with no prior exposure to combinatorics will find enough introductory material to quickly get a grasp of what combinatorics is all about and acquire the confidence to start tackling problems.

As we collect more problems, we'll add them to a supplementary problems pdf file.

About the authors

Stefan Hollos and J. Richard Hollos are physicists and electrical engineers by training, and enjoy anything related to math, physics, engineering and computing. They are brothers and business partners at Exstrom Laboratories LLC in Longmont, Colorado.

Table of Contents

• Preface to Second Edition
• Preface to First Edition
• Introduction to Combinatorics
• Definitions
• Set Enumeration
• Sum Rule
• Product Rule
• Permutations
• Combinations
• Multinomial Coefficients
• Balls in Boxes
• Inclusion Exclusion Principle
• Pigeon Hole Principle
• Stirling Numbers of the Second Kind
• Bell Numbers
• Integer Partitions
• The Twelve Fold Way
• Problems
• Further Reading