Authors:
- A short, compact yet comprehensive introduction to Catalan numbers and their applications
- Designed to be as accessible for students as possible
- Includes exercises with hints and solutions to help students gain a better grasp on the material
Part of the book series: Compact Textbooks in Mathematics (CTM)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
About this book
This textbook provides an introduction to the Catalan numbers and their remarkable properties, along with their various applications in combinatorics. Intended to be accessible to students new to the subject, the book begins with more elementary topics before progressing to more mathematically sophisticated topics. Each chapter focuses on a specific combinatorial object counted by these numbers, including paths, trees, tilings of a staircase, null sums in Zn+1, interval structures, partitions, permutations, semiorders, and more. Exercises are included at the end of book, along with hints and solutions, to help students obtain a better grasp of the material. The text is ideal for undergraduate students studying combinatorics, but will also appeal to anyone with a mathematical background who has an interest in learning about the Catalan numbers.
“Roman does an admirable job of providing an introduction to Catalan numbers of a different nature from the previous ones. He has made an excellent choice of topics in order to convey the flavor of Catalan combinatorics. [Readers] will acquire a good feeling for why so many mathematicians are enthralled by the remarkable ubiquity and elegance of Catalan numbers.”
 - From the foreword by Richard Stanley
Reviews
“The pace of this book is of an introductory nature, the coverage of Catalan numbers is rigorous and will provide the reader with a firm grasp of many of the properties of these numbers. … a scholarly work and one that number theorists will find well worth reading.” (James Van Speybroeck, Computing Reviews, April, 2016)
“The book is supplemented by a set of exercises for those who want to go further. The reader is helped by 70 carefully designed figures throughout the book. The 24 enumeration problems are selected carefully to show Catalan numbers from very different viewpoints. Several of these problems likely have their most readable write-up in this book. A must for anyone, who wants to understand the significance of Catalan numbers!” (László Székely, zbMATH 1342.05002, 2016)
Authors and Affiliations
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California State University, Fullerton , IRVINE, USA
Steven Roman
About the author
Bibliographic Information
Book Title: An Introduction to Catalan Numbers
Authors: Steven Roman
Series Title: Compact Textbooks in Mathematics
DOI: https://doi.org/10.1007/978-3-319-22144-1
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author 2015
Hardcover ISBN: 978-3-319-22143-4Published: 24 November 2015
Softcover ISBN: 978-3-319-37401-7Published: 23 August 2016
eBook ISBN: 978-3-319-22144-1Published: 17 November 2015
Series ISSN: 2296-4568
Series E-ISSN: 2296-455X
Edition Number: 1
Number of Pages: XII, 121
Number of Illustrations: 44 b/w illustrations
Topics: Combinatorics, Graph Theory, Sequences, Series, Summability, Mathematical Applications in Computer Science, Discrete Mathematics in Computer Science