CONTEMPORARY MATHEMATICS 495 /À « V> Ê> `Ê `i « Ìi ÌÊ >Ì i >Ì Và ÌiÀ >Ì > Ê7 À à «Ê/,"* äÇ /À « V> Ê> `Ê `i « Ìi ÌÊ >Ì i >Ì VÃÊ Õ}ÕÃÌÊÓxqÎä]ÊÓääÇ `i«i `i ÌÊ1 ÛiÀà ÌÞÊ vÊ ÃV ÜÊ > `Ê >L À>Ì ÀÞÊ ° 6°Ê* Vi iÌ °Ê °Ê ÌÛ ÛÊ -°Ê °Ê-iÀ}iiÛ ` Ì Àà American Mathematical Society Tropical and Idempotent Mathematics This page intentionally left blank CONTEMPORARY MATHEMATICS 495 Tropical and Idempotent Mathematics International Workshop TROPICAL-07 Tropical and Idempotent Mathematics August 25–30, 2007 Independent University of Moscow and Laboratory J.-V. Poncelet G. L. Litvinov S. N. Sergeev Editors American Mathematical Society Providence, Rhode Island Editorial Board Dennis DeTurck, managing editor George Andrews Abel Klein Martin J. Strauss 2000 Mathematics Subject Classification. Primary 06–06, 06F07, 14A99, 15–06, 16Y60, 46N99, 46T99, 49L99, 81P05, 91B70. Library of Congress Cataloging-in-Publication Data International Workshop Tropical-07 (2007 : Moscow, Russia) Tropical and idempotent mathematics : International Workshop Tropical-07, August 25– 30, 2007, Independent University of Moscow and French-Russian Laboratory “J.-V. Poncelet,” Moscow, Russia / G.L. Litvinov, S.N. Sergeev, editors. p. cm. — (Contemporary mathematics ; v. 495) Includes bibliographical references. ISBN 978-0-8218-4782-4 (alk. paper) 1. Idempotents—Congresses. 2. Tropical geometry—Congresses. 3. Mathematical physics— Congresses. I. Litvinov, G. L. (Grigorii Lazarevich), 1944– II. Sergeev, S. N., 1981– III. Title. QC20.7.I33I58 516.3′5—dc22 2007 2009011257 Copying and reprinting. Material in this book may be reproduced by any means for educational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents and provided that the customary acknowledgment of the source is given. This consent does not extend to other kinds of copying for general distribution, for advertising or promotional purposes, or for resale. Requests for permission for commercial use of material should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294, USA. Requests can also be made by e-mail to
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