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008 120119s2012 nju ob 001 0 eng d
020 _a9781118159743
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020 _a1118159748
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020 _a1118159772
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020 _a9781118159767
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020 _a1118159764
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035 _a(OCoLC)773301897
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037 _a10.1002/9781118159743
_bWiley InterScience
_nhttp://www3.interscience.wiley.com
037 _a65521384-B8D5-48C9-B4EF-70C8CB1F3062
_bOverDrive, Inc.
_nhttp://www.overdrive.com
040 _aDG1
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049 _aMAIN
050 4 _aQA241
_b.G725 2012
072 7 _aMAT
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082 0 4 _a512.7/2
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084 _aMAT036000
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084 _a31.14
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084 _a31.12
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100 1 _aGrimaldi, Ralph P.
245 1 0 _aFibonacci and catalan numbers : an introduction /
_cRalph P. Grimaldi.
_h[electronic resource]
260 _aHoboken, N.J. :
_bJohn Wiley & Sons,
_c©2012.
300 _a1 online resource
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _adata file
_2rda
380 _aBibliography
504 _aIncludes bibliographical references and index.
505 0 _aFrontmatter -- 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"--
_cProvided by publisher.
588 0 _aPrint version record.
650 0 _aFibonacci numbers.
650 0 _aRecurrent sequences (Mathematics)
650 0 _aCatalan numbers (Mathematics)
650 0 _aCombinatorial analysis.
650 4 _aMATHEMATICS
_xCombinatorics.
650 7 _aMATHEMATICS
_xCombinatorics.
_2bisacsh
650 7 _aCatalan numbers (Mathematics)
_2fast
_0(OCoLC)fst01746088
650 7 _aCombinatorial analysis.
_2fast
_0(OCoLC)fst00868961
650 7 _aFibonacci numbers.
_2fast
_0(OCoLC)fst00923656
650 7 _aRecurrent sequences (Mathematics)
_2fast
_0(OCoLC)fst01091981
655 4 _aElectronic books.
655 0 _aElectronic books.
776 0 8 _iPrint version:
_aGrimaldi, Ralph P.
_tFibonacci and catalan numbers.
_dHoboken, N.J. : John Wiley & Sons, ©2012
_z9780470631577
_w(DLC) 2011043338
_w(OCoLC)744299345
856 4 0 _uhttp://onlinelibrary.wiley.com/book/10.1002/9781118159743
_zWiley Online Library
942 _2ddc
_cBK
999 _c205515
_d205515