An Introduction to Catalan Numbers

by Steven Roman (Author)
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

From the Back Cover
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

About the Author
Steven Roman is Professor Emeritus of Mathematics at California State University Fullerton.

Number of Illustrations and Tables
44 illus.
Topics
Combinatorics
Graph Theory
Sequences, Series, Summability
Mathematical Applications in Computer Science
Discrete Mathematics in Computer Science

More info and Hardcover at Springer

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