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
| ISBN: | 9783319221434 |
| Publication date: | 24th November 2015 |
| Author: | Steven Roman |
| Publisher: | Birkhauser an imprint of Springer International Publishing |
| Format: | Hardback |
| Pagination: | 121 pages |
| Series: | Compact Textbooks in Mathematics |
| Genres: |
Discrete mathematics Maths for computer scientists Calculus and mathematical analysis Combinatorics and graph theory Mathematical theory of computation |
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
An Introduction to Catalan Numbers features in the following genres: Discrete mathematics, Maths for computer scientists, Calculus and mathematical analysis, Combinatorics and graph theory, Mathematical theory of computation
Paperback, Hardback. Not Available.
An Introduction to Catalan Numbers was written by Steven Roman and published by Birkhauser an imprint of Springer International Publishing
An Introduction to Catalan Numbers has 121 pages
Yes it is part of Compact Textbooks in Mathematics series