Combinatorial Reasoning: An Introduction to the Art of Counting

Written by well-known scholars in the field, this book introduces combinatorics alongside modern techniques, showcases the interdisciplinary aspects of the topic, and illustrates how to problem solve with a multitude of exercises throughout. The authors’ approach is very reader-friendly and avoids the “scholarly tone” found in many books on this topic.

Combinatorial Reasoning: An Introduction to the Art of Counting:

• Focuses on enumeration and combinatorial thinking as a way to develop a variety of effective approaches to solving counting problems
• Includes brief summaries of basic concepts from probability, power series, and group theory to show how combinatorics interacts with other fields
• Provides abstract ideas that are grounded in familiar concrete settings and features plentiful diagrams throughout to further add in reader understanding
• Presents simple and helpful notations as needed, and simple cases are treated first before more general and/or advanced cases
• Contains over 700 exercise sets, ranging from the routine to the advanced, with either hints, short answers, or complete solutions for odd numbered problems.  An Instructor’s Manual (available via request to the Publisher) provides complete solutions for all exercises

Table of Contents

Part I The Basics of Enumerative Combinatorics
Chapter 1 Initial Encounters with Combinatorial Reasoning
Chapter 2 Selections, Arrangements, and Distributions
Chapter 3 Binomial Series and Generating Functions
Chapter 4 Alternating Sums, Inclusion-Exclusion Principle, Rook Polynomials, and Fibonacci Nim
Chapter 5 Recurrence Relations
Chapter 6 Special Numbers

Part II Two Additional Topics in Enumeration
Chapter 7 Linear Spaces and Recurrence Sequences
Chapter 8 Counting with Symmetries

Part III Notations Index, Appendices, and Solutions to Selected Odd Problems

Appendix A: Mathematical Induction
Appendix B: Searching the Online Encyclopedia of Integer Sequences (OEIS)
Appendix C: Generalized Vandermonde Determinants