An Introduction To Catalan Numbers - Roman Steven | Libro Birkhäuser 11/2015 - HOEPLI.it

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# An Introduction to Catalan Numbers

## roman steven

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## Dettagli

Genere:Libro
Lingua: Inglese
Pubblicazione: 11/2015
Edizione: 1st ed. 2015

## Trama

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

## Sommario

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.

## Autore

Steven Roman is Professor Emeritus of Mathematics at California State University Fullerton.  He is the author of numerous other mathematics textbooks, including Field Theory (2006), Advanced Linear Algebra(2008), Fundamentals of Group Theory (2012), Introduction to the Mathematics of Finance (2012), and An Introduction to Catalan Numbers (2015).

## Altre Informazioni

ISBN:

### 9783319221434

Condizione: Nuovo
Collana: Compact Textbooks in Mathematics
Dimensioni: 235 x 155 mm Ø 3317 gr
Formato: Copertina rigida
Illustration Notes:44 Illustrations, black and white
Pagine Arabe: 121
Pagine Romane: xii

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