An Introduction to Catalan Numbers
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 top
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Steven Roman
An Introduction to Catalan Numbers
Compact Textbooks in Mathematics
Compact Textbooks in Mathematics This textbook series presents concise introductions to current topics in mathematics and mainly addresses advanced undergraduates and master students. The concept is to offer small books covering subject matter equivalent to 2- or 3hour lectures or seminars which are also suitable for self-study. The books provide students and teachers with new perspectives and novel approaches. They feature examples and exercises to illustrate key concepts and applications of the theoretical contents. The series also includes textbooks specifically speaking to the needs of students from other disciplines such as physics, computer science, engineering, life sciences, finance.
More information about this series at http://www.springer.com/series/11225
Steven Roman
An Introduction to Catalan Numbers
Steven Roman Professor Emeritus California State University, Fullerton Irvine, CA, USA
ISSN 2296-4568 ISSN 2296-455X (electronic) Compact Textbooks in Mathematics ISBN 978-3-319-22143-4 ISBN 978-3-319-22144-1 (eBook) DOI 10.1007/978-3-319-22144-1 Library of Congress Control Number: 2015952313 Mathematics Subject Classification (2010): 05A05, 05A15, 05A18, 05C05, 05C30, 05C38, 05C75 Springer Cham Heidelberg New York Dordrecht London # The Author 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Cover design: deblik, Berlin Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)
To Scott and to Greg Re´quiem æte´rnam dona eis, requie´scant in pace.
Foreword
There have been many recent expositions of the fascinating sequence 1, 1, 2, 5, 14, 42, . . . of Catalan numbers. Indeed, I myself have just completed a monograph on this topic. Steven Roman does an admirable job of providing an introduction to Catalan numbers of a different nature from the previous ones. In particular, he gives complet
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