An Introduction to Catalan Numbers

Steven Roman

ISBN 10: 331937401X / ISBN 13: 9783319374017

Editore: Springer International Publishing, Springer International Publishing Aug 2016, 2016

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Neuware -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.

Codice articolo 9783319374017

Dati bibliografici

• Titolo: An Introduction to Catalan Numbers
• Editore: Springer International Publishing, Springer International Publishing Aug 2016
• Data di pubblicazione: 2016
• Lingua: Inglese
• ISBN 10: 331937401X
• ISBN 13: 9783319374017
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 8 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 8 millimetri di profondità
• Peso: 219 grammi

Descrizione articolo

Riassunto

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 Z_n+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

Informazioni sull?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).