تولید تابع‌شناسی

This is the Second Edition of the highly successful introduction to the use of generating functions and series in combinatorial mathematics. This new edition includes several new areas of application, including the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences. An appendix on using the computer algebra programs MAPLE(r) and Mathematica (r) to generate functions is also included. The book provides a clear, unified introduction to the basic enumerative applications of generating functions, and includes exercises and solutions, many new, at the end of each chapter. Provides new applications on the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences Features an Appendix on using MAPLE(r) and Mathematica (r) to generate functions Includes many new exercises with complete solutions at the end of each chapter Annotation This is the Second Edition of the highly successful introduction to the use of generating functions and series in combinatorial mathematics. This new edition includes several new areas of application, including the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences. An appendix on using the computer algebra programs MAPLE(r) and Mathematica(r) to generate functions is also included. The book provides a clear, unified introduction to the basic enumerative applications of generating functions, and includes exercises and solutions, many new, at the end of each chapter.Key Features* Provides new applications on the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences* Features an Appendix on using MAPLE(r) and Mathematica (r) to generate functions* Includes many new exercises with complete solutions at the end of each chapter Content: Front Matter , Page iii Copyright , Page iv Preface , Page vii Preface to the Second Edition , Page ix Chapter 1 - Introductory ideas and examples , Pages 1-29 Chapter 2 - Series , Pages 30-72 Chapter 3 - Cards, Decks, and Hands: The Exponential Formula , Pages 73-107 Chapter 4 - Applications of generating functions , Pages 108-166 Chapter 5 - Analytic and asymptotic methods , Pages 167-191 Appendix - Using Maple and Mathematica , Pages 192-196 Solutions , Pages 197-223 References , Pages 224-226 Index , Pages 227-228