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An Introduction to Catalan Numbers

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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

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Detail Information

Series Title

Compact Textbooks in Mathematics

Call Number

519.6 ROM i

Publisher

Cham, Switzerland : Birkhäuser Cham., 2015

Collation

XII, 121

Language

English

ISBN/ISSN

978-3-319-22144-1

Classification

519.6

Content Type

text

Media Type

computer

Carrier Type

online resource

Edition

Ed. 1

Subject(s)

Discrete Mathematics
Graph Theory

Specific Detail Info

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Statement of Responsibility

Steven Roman

Other Information

Cataloger

umi

Source

https://link.springer.com/content/pdf/10.1007/978-3-319-22144-1.pdf?pdf=button

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