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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.)

Fibonacci and catalan numbers = an introduction /
Grimaldi, Ralph P.

Fibonacci and catalan numbersan introduction /[electronic resource] :Ralph P. Grimaldi. - Hoboken, N.J. :John Wiley & Sons,c2012. - 1 online resource.

Includes bibliographical references and index.

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.

"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. Starting with a historical background on the topic, the author goes on to present the properties of Fibonacci numbers, a slew of introductory-level examples, and in-depth discussion of related topics including compositions and palindromes; tiling and Fibonacci numbers; solving linear recurrence relations; graph theory; Lucas numbers; and alternate Fibonacci numbers. The second half of the book explores Catalan numbers, and the author builds a complete foundation to the topic using a historical background and introductory examples, along with coverage of partial orders, total orders, topological sorting, graph theory, rooted ordered binary trees, pattern avoidance, and the Narayana numbers. Coverage of both topics are accompanied by interesting, real-world examples from areas such as sports, botany, and computer science. Each section concludes with detailed exercise sets that can also serve as extended examples of the presented material along with selected solutions. An Instructor's Manual featuring complete solutions is available upon written request, and extensive reference sections outline resources for further study of the discussed topics"--

ISBN: 9781118159743 (electronic bk.)

Standard No.: 9786613401151

Publisher. No.: EB00062802Recorded BooksSubjects--Topical Terms:

589041
Fibonacci numbers.

LC Class. No.: QA241 / .G725 2012

Dewey Class. No.: 512.7/2

Fibonacci and catalan numbers = an introduction /
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245 1 0 $a Fibonacci and catalan numbers $h [electronic resource] : $b an introduction / $c Ralph P. Grimaldi.
260 $a Hoboken, N.J. : $b John Wiley & Sons, $c c2012.
300 $a 1 online resource.
504 $a Includes bibliographical references and index.
505 0 $a 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.
520 $a "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. Starting with a historical background on the topic, the author goes on to present the properties of Fibonacci numbers, a slew of introductory-level examples, and in-depth discussion of related topics including compositions and palindromes; tiling and Fibonacci numbers; solving linear recurrence relations; graph theory; Lucas numbers; and alternate Fibonacci numbers. The second half of the book explores Catalan numbers, and the author builds a complete foundation to the topic using a historical background and introductory examples, along with coverage of partial orders, total orders, topological sorting, graph theory, rooted ordered binary trees, pattern avoidance, and the Narayana numbers. Coverage of both topics are accompanied by interesting, real-world examples from areas such as sports, botany, and computer science. Each section concludes with detailed exercise sets that can also serve as extended examples of the presented material along with selected solutions. An Instructor's Manual featuring complete solutions is available upon written request, and extensive reference sections outline resources for further study of the discussed topics"-- $c Provided by publisher.
588 $a Description based on print version record.
650 0 $a Fibonacci numbers. $3 589041
650 0 $a Recurrent sequences (Mathematics) $3 950291
650 0 $a Catalan numbers (Mathematics) $3 943575
650 0 $a Combinatorial analysis. $3 523878
710 2 $a Wiley InterScience (Online service) $3 1597786
856 4 0 $u http://onlinelibrary.wiley.com/book/10.1002/9781118159743