An Introduction to Catalan Numbers

• Main Author: Roman, Steven (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2015.
• Edition: 1st ed. 2015.
• Series: Compact Textbooks in Mathematics,
• Subjects: Mathematics.; Computer science > Mathematics.; Sequences (Mathematics).; Computer mathematics.; Combinatorics.; Graph theory.; Graph Theory.; Sequences, Series, Summability.; Mathematical Applications in Computer Science.; Discrete Mathematics in Computer Science.

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 soph...

Table of Contents:

• Introduction
• Dyck Words
• The Catalan Numbers
• Catalan Numbers and Paths
• Catalan Numbers and Trees
• Catalan Numbers and Geometric Widgits
• Catalan Numbers and Algebraic Widgits
• Catalan Numbers and Interval Structures
• Catalan Numbers and Partitions
• Catalan Numbers and Permutations
• Catalan Numbers and Semiorders
• Exercises
• Solutions and Hints
• Appendix A: A Brief Introduction to Partially Ordered Sets
• Appendix B: A Brief Introduction to Graphs and Trees
• Index.