Fibonacci and catalan numbers : an introduction /

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"In this one-of-a-kind book, Ralph Grimaldi uses his extensive experience from the classroom and as a leader of mini-courses to present an accessible, single resource on the topics of Fibonacci Numbers and Catalan Numbers. The book first embarks on a complete treatment of Fibonacci numbers. Sta...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Grimaldi, Ralph P.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Hoboken, N.J. : John Wiley & Sons, ©2012.
Temas:
Fibonacci numbers.
Recurrent sequences (Mathematics)
Catalan numbers (Mathematics)
Combinatorial analysis.
Suites de Fibonacci.
Suites récurrentes (Mathématiques)
Nombres de Catalan.
Analyse combinatoire.
MATHEMATICS > Combinatorics.
Acceso en línea:Texto completo (Requiere registro previo con correo institucional)
Tabla de Contenidos:
  • Frontmatter
  • The Fibonacci Numbers. Historical Background
  • The Problem of the Rabbits
  • The Recursive Definition
  • Properties of the Fibonacci Numbers
  • Some Introductory Examples
  • Compositions and Palindromes
  • Tilings: Divisibility Properties of the Fibonacci Numbers
  • Chess Pieces on Chessboards
  • Optics, Botany, and the Fibonacci Numbers
  • Solving Linear Recurrence Relations: The Binet Form for
  • More on and : Applications in Trigonometry, Physics, Continued Fractions, Probability, the Associative Law, and Computer Science
  • Examples from Graph Theory: An Introduction to the Lucas Numbers
  • The Lucas Numbers: Further Properties and Examples
  • Matrices, The Inverse Tangent Function, and an Infinite Sum
  • The gcd Property for the Fibonacci Numbers
  • Alternate Fibonacci Numbers
  • One Final Example?
  • The Catalan Numbers. Historical Background
  • A First Example: A Formula for the Catalan Numbers
  • Some Further Initial Examples
  • Dyck Paths, Peaks, and Valleys
  • Young Tableaux, Compositions, and Vertices and Arcs
  • Triangulating the Interior of a Convex Polygon
  • Some Examples from Graph Theory
  • Partial Orders, Total Orders, and Topological Sorting
  • Sequences and a Generating Tree
  • Maximal Cliques, a Computer Science Example, and the Tennis Ball Problem
  • The Catalan Numbers at Sporting Events
  • A Recurrence Relation for the Catalan Numbers
  • Triangulating the Interior of a Convex Polygon for the Second Time
  • Rooted Ordered Binary Trees, Pattern Avoidance, and Data Structures
  • Staircases, Arrangements of Coins, The Handshaking Problem, and Noncrossing Partitions
  • The Narayana Numbers
  • Related Number Sequences: The Motzkin Numbers, The Fine Numbers, and the Schr̲der Numbers
  • Generalized Catalan Numbers
  • One Final Example?
  • Solutions for the Odd-Numbered Exercises
  • Index.

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