Notes on Introductory Combinatorics 9780817649524, 9780817649531

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Modern Birkh¨ auser Classics Many of the original research and survey monographs in pure and applied mathematics published by Birkh¨ auser in recent decades have been groundbreaking and have come to be regarded as foundational to the subject. Through the MBC Series, a select number of these modern classics, entirely uncorrected, are being re-released in paperback (and as eBooks) to ensure that these treasures remain accessible to new generations of students, scholars, and researchers.

For other titles published in this series, go to www.springer.com/series/7588

´ George Polya Robert E. Tarjan Donald R. Woods

Notes on Introductory Combinatorics

Reprint of the 1983 Edition Birkh¨auser Boston • Basel • Berlin

George P´olya (Deceased) Department of Mathematics Stanford University Stanford, CA 94305 USA

Robert E. Tarjan Department of Computer Science Princeton University Princeton, NJ 08544 USA

Donald R. Woods Google Inc. 1600 Amphitheatre Parkway Mountain View, CA 94043 USA

Originally published in the series Progress in Computer Science and Applied Logic

ISBN 978-0-8176-4952-4 e-ISBN 978-0-8176-4953-1 DOI 10.1007/978-0-8176-4953-1 Library of Congress Control Number: 2009938715 Mathematics Subject Classification (2000): 05A15, 05C45, 05D10, 20Bxx, 68R05 c Birkh¨auser Boston, a part of Springer Science+Business Media, LLC 2010 

All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Birkh¨auser Boston, c/o Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Birkh¨auser Boston is a part of Springer Science+Business Media (www.birkhauser.com)

G. Pólya et al., Notes on Introductory Combinatorics, Modern Birkhäuser Classics, DOI 10.1007/978-0-8176-4953-1_1, © Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2010

G. Pólya et al., Notes on Introductory Combinatorics, Modern Birkhäuser Classics, DOI 10.1007/978-0-8176-4953-1_2, © Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2010

G. Pólya et al., Notes on Introductory Combinatorics, Modern Birkhäuser Classics, DOI 10.1007/978-0-8176-4953-1_3, © Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2010

G. Pólya et al., Notes on Introductory Combinatorics, Modern Birkhäuser Classics, DOI 10.1007/978-0-8176-4953-1_4, © Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2010

G. Pólya et al., Notes on Introductory Combinatorics, Modern Birkhäuser Classics, DOI 10.1007/978-0-8176-4953-1_5, © Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2010

G. Pólya et al., Notes on Introductory Combinatorics, Modern Birkhäuser Classics, DOI 10.1007/978-0-8176-4953-1_6, © Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2010

G. Pólya et al., Notes on Introductory Combinatorics, Modern Birkhäuser Classics, DOI 10.1007/978-0-8176-4953-1_7, © Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2010

G. Pólya et al., Notes on Introductory Combinatorics, Modern Birkhäuser Classics, DOI 10.1007/978-0-8176-4953-1_8, © Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2010

G. Pólya et al., Notes on Introductory Combinatorics, Modern Birkhäuser Classics, DOI 10.1007/978-0-8176-4953-1_9, © Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2010

G. Pólya et al., Notes on Introductory Combinatorics, Modern Birkhäuser Classics, DOI 10.1007/978-0-8176-4953-1_10, © Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2010

G. Pólya et al., Notes on Introductory Combinatorics, Modern Birkhäuser Classics, DOI 10.1007/978-0-8176-4953-1_11, © Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2010

G. Pólya et al., Notes on Introductory Combinatorics, Modern Birkhäuser Classics, DOI 10.1007/978-0-8176-4953-1_12, © Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2010

G. Pólya et al., Notes on Introductory Combinatorics, Modern Birkhäuser Classics, DOI 10.1007/978-0-8176-4953-1_13, © Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2010

G. Pólya et al., Notes on Introductory Combinatorics, Modern Birkhäuser Classics, DOI 10.1007/978-0-8176-4953-1_14, © Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2010

G. Pólya et al., Notes on Introductory Combinatorics, Modern Birkhäuser Classics, DOI 10.1007/978-0-8176-4953-1_15, © Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2010

G. Pólya et al., Notes on Introductory Combinatorics, Modern Birkhäuser Classics, DOI 10.1007/978-0-8176-4953-1_16, © Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2010