Combinatorial reasoning : an introduction to the art of counting / Duane DeTemple, William Webb.
- Hoboken, New Jersey : Wiley, 2014.
1 online resource (484 p.)
- Combinatorial analysis -- Textbooks.
Mathematical analysis -- Textbooks.
- Electronic books.
- 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 problemsIncludes b
- Combinatorial Reasoning; Contents; Preface; Features of This Text; Flexibility for Courses; Part I The Basics of Enumerative Combinatorics; 1 Initial Encounters with Combinatorial Reasoning; 1.1 Introduction; 1.2 The Pigeonhole Principle; 1.2.1 Applications to Ranges and Domains of Functions; 1.2.2 An Application to the Chinese Remainder Theorem; 1.2.3 Generalizations of the Pigeon Principle; Problems; 1.3 Tiling Chessboards with Dominoes; Problems; 1.4 Figurate Numbers; 1.4.1 More General Polygonal Numbers; Problems; 1.5 Counting Tilings of Rectangles
2.3 Combinatorial Models2.3.1 Tiling Models; 2.3.2 Block Walking Models; 2.3.3 The Committee Selection Model; 2.3.4 The Flagpole Model; Problems; 2.4 Permutations and Combinations with Repetitions; 2.4.1 Multisets; 2.4.2 Permutations with Repetition; 2.4.3 Combinations with Repetition; Problems; 2.5 Distributions to Distinct Recipients; 2.5.1 Distributions of Distinct Objects to Distinct Recipients; 2.5.2 Distributions of Identical Objects to Distinct Recipients; 2.5.3 Mixed Distribution Problems; 2.5.4 Equations for Distributions; 2.5.5 Counting Functions; Problems
2.6 Circular Permutations and Derangements2.6.1 Circular Permutations; 2.6.2 Derrangements; Problems; 2.7 Summary and Additional Problems; Problems; Reference; 3 Binomial Series and Generating Functions; 3.1 Introduction; 3.2 The Binomial and Multinomial Theorems; 3.2.1 The Binomial Theorem; 3.2.2 The Multinomial Theorem; Problem; 3.3 Newtons Binomial Series; 3.3.1 Generating Function for the Multichoose Coefficients; 3.3.2 Generalized Binomial Coefficients and Newtons Binomial Series; Problem; 3.4 Ordinary Generating Functions; 3.4.1 Deriving Ordinary Generating Functions
3.4.2 Products of Ordinary Generating Functions3.4.3 Counting with Ordinary Generating Functions; Problem; 3.5 Exponential Generating Functions; 3.5.1 Deriving Exponential Generating Functions; 3.5.2 Products of Exponential Generating Functions; 3.5.3 Counting with Exponential Generating Functions; 3.5.4 Comparison between Exponential and Ordinary Generating Functions; Problems; 3.6 Summary and Additional Problems; Problems; References; 4 Alternating Sums, Inclusion-Exclusion Principle, Rook Polynomials, and Fibonacci Nim; 4.1 Introduction; 4.2 Evaluating Alternating Sums with the DIE Method
4.2.1 Using the DIE Method
- Description based upon print version of record.
Includes bibliographical references at the end of each chapters and index.
Description based on print version record.
- Webb, William, 1944- author.
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