Fibonacci and catalan numbers = an i...
Grimaldi, Ralph P.

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  • Fibonacci and catalan numbers = an introduction /
  • 紀錄類型: 書目-電子資源 : Monograph/item
    正題名/作者: Fibonacci and catalan numbers/ Ralph P. Grimaldi.
    其他題名: an introduction /
    作者: Grimaldi, Ralph P.
    出版者: Hoboken, N.J. :John Wiley & Sons, : c2012.,
    面頁冊數: 1 online resource.
    內容註: 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.
    標題: Fibonacci numbers. -
    電子資源: http://onlinelibrary.wiley.com/book/10.1002/9781118159743
    ISBN: 9781118159743 (electronic bk.)
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