Combinatorics A Problem-Based Approach
This text provides a theoretical background for several topics in combinatorial mathematics, such as enumerative combinatorics (including partitions and Burnside's lemma), magic and Latin squares, graph theory, extremal combinatorics, mathematical games a
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Pavle Mladenović
Combinatorics A Problem-Based Approach
Problem Books in Mathematics Series Editor: Peter Winkler Department of Mathematics Dartmouth College Hanover, NH 03755 USA
More information about this series at http://www.springer.com/series/714
Pavle Mladenovi´c
Combinatorics A Problem-Based Approach
123
Pavle Mladenovi´c Faculty of Mathematics University of Belgrade Belgrade, Serbia
ISSN 0941-3502 ISSN 2197-8506 (electronic) Problem Books in Mathematics ISBN 978-3-030-00830-7 ISBN 978-3-030-00831-4 (eBook) https://doi.org/10.1007/978-3-030-00831-4 Library of Congress Control Number: 2018963721 c Springer Nature Switzerland AG 2019 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. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
This book is an extended version of the latest edition of my book written in Serbian under the title Combinatorics. I started gathering and selecting material and combinatorial problems for the book in the late 1980s while giving lectures to young talented mathematicians preparing for national and international mathematical competitions and while working as a jury member at the national mathematical olympiad. In the 1990s and at the beginning of this century, till 2006, I was also involved in organizing national mathematical competitions. In two five-year periods, I was leader of the team of FR Yugoslavia (Serbia and Montenegro), first at the Balkan Mathematical Olympiad (BMO 1992–1996) and then at the International Mathematical Olympiad (IMO 1997–2001) and also was a jury member at these mathematical olympiads. This engagement along with my work at the University of Belgrade had a great influence on the form and content of this book. The first Serbian edition was published in 1989, with t
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