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

COMBINATORIAL REASONING 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