Solutions Manual to accompany Combinatorial Reasoning: An Introduction to the Art of Counting

Showcases the interdisciplinary aspects of combinatorics and illustrates how to problem solve with a multitude of exercises

Written by two well-known scholars in the field, Combinatorial Reasoning: An Introduction to the Art of Counting presents a clear and comprehensive introduction to the concepts and methodology of beginning combinatorics. Focusing on modern techniques and applications, the book develops a variety of effective approaches to solving counting problems.

Balancing abstract ideas with specific topical coverage, the book utilizes real-world examples with problems ranging from basic calculations that are designed to develop fundamental concepts to more challenging exercises that allow for a deeper exploration of complex combinatorial situations. Simple cases are treated first before moving on to general and more advanced cases. Additional features of the book include:

• Approximately 700 carefully structured problems designed for readers at multiple levels, many with hints and/or short answers
• Numerous examples that illustrate problem solving using both combinatorial reasoning and sophisticated algorithmic methods
• A novel approach to the study of recurrence sequences, which simplifies many proofs and calculations
• Concrete examples and diagrams interspersed throughout to further aid comprehension of abstract concepts
• A chapter-by-chapter review to clarify the most crucial concepts covered

Combinatorial Reasoning: An Introduction to the Art of Counting is an excellent textbook for upper-undergraduate and beginning graduate-level courses on introductory combinatorics and discrete mathematics.

Preface vii

Part I The Basics of Enumerative Combinatorics

1 Initial EnCOUNTers with Combinatorial Reasoning 3

2 Selections, Arrangements, and Distributions 23

3 Binomial Series and Generating Functions 51

4 Alternating Sums, Inclusion-Exclusion Principle, Rook Polynomials, and Fibonacci Nim 77

5 Recurrence Relations 95

6 Special Numbers 129

Part II Two Additional Topics in Enumeration

7 Linear Spaces and Recurrence Sequences 161

8 Counting with Symmetries 175

DUANE DETEMPLE, PHD, is Professor Emeritus in the Department of Mathematics at Washington State University (WSU). He is the recipient of the 2007 WSU Sahlin Faculty Excellence Award for Instruction as well as the Distinguished Teaching Award from the Pacific Northwest Section of the Mathematical Association of America.

WILLIAM WEBB, PHD, is Professor in the Department of Mathematics at Washington State University and President of the Fibonacci Association. His research interests include the properties of recurrence sequences and binomial coefficients. He is the author of numerous research publications on combinatorics, number theory, fair division, and cryptography.