EAN: 9783319374017

COMPACT TEXTBOOKS IN MATHEMATICS AN INTRODUCT...

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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