ISBN-10:
019533454X
ISBN-13:
9780195334548
Pub. Date:
12/16/2008
Publisher:
Oxford University Press
Catalan Numbers with Applications

Catalan Numbers with Applications

by Thomas Koshy

Hardcover

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Product Details

ISBN-13: 9780195334548
Publisher: Oxford University Press
Publication date: 12/16/2008
Pages: 440
Product dimensions: 6.30(w) x 9.30(h) x 1.10(d)

About the Author

Thomas Koshy, Ph.D., is Professor of Mathematics at Framingham State College, Framingham, Massachusetts. His Fibonacci and Lucas Numbers with Applications, published by Wiley, won the Association of American Publishers' new book award in 2001.

Table of Contents

List of Symbols xiii

1 Binomial Coefficients 1

2 The Central Binomial Coefficient 13

3 The Central Binomial Coefficient Revisited 51

4 Binomial Coefficients Revisited 89

5 Catalan Numbers 103

6 The Ubiquity of Catalan Numbers I 149

7 The Ubiquity of Catalan Numbers II 191

8 Trees and Catalan Numbers 227

9 Lattice Paths and Catalan Numbers 259

10 Partitions and Catalan Numbers 281

11 Algebra, Sports, and Catalan Numbers 289

12 Pascal's Triangle and Catalan Numbers 313

13 Divisibility Properties 329

14 A Catalan Triangle 333

15 A Family of Binary Words 347

16 Tribinomial Coefficients 357

17 Generalized Catalan Numbers 375

Appendix A 379

A.1 Bijections 379

A.2 Fundamental Counting Principles 380

A.3 Recursion 381

A.4 Generating Functions 382

A.5 Congruences 383

A.6 Mathematical Induction 384

A.7 Extended Binomial Coefficients 385

A.8 Maclaurin's Series 386

A.9 A Definition of ([characters not reproducible]) 387

Appendix B The First 100 Catalan Numbers 391

References 395

Index of Mathematicians 409

Index 411

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