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.

Duane DeTemple is the author of Solutions Manual to accompany Combinatorial Reasoning: An Introduction to the Art of Counting, published by Wiley. William Webb is the author of Solutions Manual to accompany Combinatorial Reasoning: An Introduction to the Art of Counting, published by Wiley.

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

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