Roman S. An Introduction to Catalan Numbers

Birkhäuser Basel, 2015. — 119 p. — ISBN10: 3319221434A 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 materialThis 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.Topics
Combinatorics
Graph Theory
Sequences, Series, Summability
Mathematical Applications in Computer Science
Discrete Mathematics in Computer Science