目录 PREFACEPART ONE THE FIBONACCI NUMBERS1.Historical Background2.The Problem of the Rabbits3.The Recursive Definitio4.Properties of the Fibonacci Numbers5.Some Introductory Examples6.Compositions and Palindromes7.Tilings: Divisibility Properties of the Fibonacci Numbers8.Chess Pieces on Chesoards9.Optics, Botany, and the Fibonacci Numbers10.Solving Linear Recurrence Relations: The Binet Form for F11.More on ot and B: Applications in Trigonometry, Physics, Continued Fractions, Probability, the Associative Law, and Computer Science12.Examples from Graph Theory: An Introduction to the Lucas Numbers13.The Lucas Numbers: Further Properties and Examples14.Matrices, The Inverse Tangent Function, and an Infinite Sum15.The gcd Property for the Fibonacci Numbers16.Alternate Fibonacci Numbers17.One Final Example?PART TWO THE CATALAN NUMBERS18.Historical Background19.A First Example: A Formula for the Catalan Numbers20.Some Further Initial Examples21.Dyck Paths, Peaks, and Valleys22.Young Tableaux, Compositions, and Vertices and Arcs23.Triangulating the Interior of a Convex Polygo24.Some Examples from Graph Theory25.Partial Orders, Total Orders, and Topological Sorting26.Sequences and a Generating Tree27.Maximal Cliques, a Computer Science Example, and the Tennis Ball Problem28.The Catalan Numbers at Sporting Events29.A Recurrence Relation for the Catalan Numbers30.Triangulating the Interior of a Convex Polygon for the Second Time31.Rooted Ordered Binary Trees, Pattern Avoidance, and Data Structures32.Staircases, Arrangements of Coins, The Handshaking Problem, and Noncrossing Partitions33.The Narayana Numbers34.Related Number Sequences: The Motzkin Numbers, The Fine Numbers, and The Schr6der Numbers35.Generalized Catalan Numbers36.One Final Example?Solutions for the Odd.Numbered ExercisesIndex编辑手记 作者介绍
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