包邮斐波那契数和卡塔兰数:导论:an introduction:英文

PREFACE PART ONE THE FIBONACCI NUMBERS 1.Historical Background 2.The Problem of the Rabbits 3.The Recursive Definition 4.Properties of the Fibonacci Numbers 5.Some Introductory Examples 6.Compositions and Palindromes 7.Tilings: Divisibility Properties of the Fibonacci Numbers 8.Chess Pieces on Chessboards 9.Optics, Botany, and the Fibonacci Numbers 10.Solving Linear Recurrence Relations: The Binet Form for Fn 11.More on ot and B: Applications in Trigonometry, Physics, Continued Fractions, Probability, the Associative Law, and Computer Science 12.Examples from Graph Theory: An Introduction to the Lucas Numbers 13.The Lucas Numbers: Further Properties and Examples 14.Matrices, The Inverse Tangent Function, and an Infinite Sum 15.The gcd Property for the Fibonacci Numbers 16.Alternate Fibonacci Numbers 17.One Final Example? PART TWO THE CATALAN NUMBERS 18.Historical Background 19.A First Example: A Formula for the Catalan Numbers 20.Some Further Initial Examples 21.Dyck Paths, Peaks, and Valleys 22.Young Tableaux, Compositions, and Vertices and Arcs 23.Triangulating the Interior of a Convex Polygon 24.Some Examples from Graph Theory 25.Partial Orders, Total Orders, and Topological Sorting 26.Sequences and a Generating Tree 27.Maximal Cliques, a Computer Science Example, and the Tennis Ball Problem 28.The Catalan Numbers at Sporting Events 29.A Recurrence Relation for the Catalan Numbers 30.Triangulating the Interior of a Convex Polygon for the Second Time 31.Rooted Ordered Binary Trees, Pattern Avoidance, and Data Structures 32.Staircases, Arrangements of Coins, The Handshaking Problem, and Noncrossing Partitions 33.The Narayana Numbers 34.Related Number Sequences: The Motzkin Numbers, The Fine Numbers, and The Schr6der Numbers 35.Generalized Catalan Numbers 36.One Final Example? Solutions for the Odd.Numbered Exercises Index 编辑手记