Associahedra, Tamari Lattices and Related Structures Tamari Memorial
Tamari lattices originated from weakenings or reinterpretations of the familar associativity law. This was the subject of Dov Tamari's thesis at the Sorbonne in Paris in 1951 and the central theme of his subsequent mathematical work. Tamari lattices
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Series Editors Hyman Bass Joseph Oesterlé Yuri Tschinkel Alan Weinstein
Folkert Müller-Hoissen Jean Marcel Pallo Jim Stasheff Editors
Associahedra, Tamari Lattices and Related Structures Tamari Memorial Festschrift
Editors Folkert Müller-Hoissen Max-Planck-Institute for Dynamics and Self-Organization Göttingen Germany
Jean Marcel Pallo Département d’Informatique, LE2I Université de Bourgogne Dijon France
Jim Stasheff Department of Mathematics University of North Carolina Chapel Hill, NC USA
ISBN 978-3-0348-0404-2 ISBN 978-3-0348-0405-9 (eBook) DOI 10.1007/978-3-0348-0405-9 Springer Basel Heidelberg New York Dordrecht London Library of Congress Control Number: 2012942603 © Springer Basel 2012 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein.
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Preface
On the occasion of the centennial birthday of the mathematician Dov Tamari (1911– 2006), born as the German Bernhard Teitler, this book commemorates his ground breaking work resulting in an associativity theory, with important contributions to the “word (decision) problem”, as well as lattice theory and geometric combinatorics. The editors of this book invited designated researchers to present modern areas of mathematics that are related to Tamari’s work. To a monomial (word) formed from a set
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