Combinatorial reasoning : an introduction to the art of counting / Duane DeTemple, William Webb.

DeTemple, Duane W., author.
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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