Polygons, Polyominoes and Polycubes
This unique book gives a comprehensive account of new mathematical tools used to solve polygon problems. In the 20th and 21st centuries, many problems in mathematics, theoretical physics and theoretical chemistry – and more recently in molecular biology a
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Lecture Notes in Physics The series Lecture Notes in Physics (LNP), founded in 1969, reports new developments in physics research and teaching – quickly and informally, but with a high quality and the explicit aim to summarize and communicate current knowledge in an accessible way. Books published in this series are conceived as bridging material between advanced graduate textbooks and the forefront of research and to serve three purposes:
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Anthony J. Guttman (Ed.)
Polygons, Polyominoes and Polycubes
Professor Anthony J. Guttman Department of Mathematics and Statistics, The University of Melbourne, Victoria, 3010 Australia
Library of Congress Control Number: 2009921794
ISSN 0075-8450 ISBN-13 978-1-4020-9926-7 (HB) ISBN-13 978-1-4020-9927-4 (e-book)
Published by Springer Science + Business Media B.V. P.O. Box 17, 3300 AA Dordrecht, The Netherlands In association with Canopus Academic Publishing Limited, 15 Nelson Parade, Bristol BS3 4HY, UK
www.springer.com and www.canopusbooks.com
All Rights Reserved © 2009 Canopus Academic Publishing Limited No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.
To the memory of two distinguished scientists and wonderful colleagues, Pierre Leroux and Oded Schramm.
Preface
The problem of counting the number of self-avoiding polygons on a square grid, either by their perimeter or their enclosed area, is a problem that is so easy to state that, at first sight, it seems surprising that it hasn’t been solved. It is however perhaps the simplest member of a large class of suc
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