Enumerative Combinatorics
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The Wadsworth & Brooks/Cole Mathematics Series Series Editors Raoul H. Bott, Harvard University David Eisenbud, Brandeis University Hugh L. Montgomery, University of Michigan Paul J. Sally, Jr., University of Chicago Barry Simon, California Institute of Technology Richard P. Stanley, Massachusetts Institute of Technology M. Adams, V. Guillemin, Measure Theory and Probability W. Beckner, A. Calder6n, R. Fefferman, P. Jones, Conferenee on Harmonie Analysis in Honor 0/ Antoni Zygmund G. Chartrand, L. Lesniak, Graphs and Digraphs, Seeond Edition J. Cochran, Applied Mathematies: Prineiples, Teehniques, and Applieations W. Derrick, Complex Analysis and Applieations, Seeond Edition J. Dieudonne, History 0/ Algebraie Geometry R. Durrett, Brownian Motion and Martingales in Analysis S. Fisher, Complex Variables A. Garsia, Topies in Almost Everywhere Convergenee R. Salem, Algebraie Numbers and Fourier Analysis, and L. Carleson, Seleeted Problems on Exeeptional Sets R. Stanley, Enumerative Combinatories, Volume I K. Stromberg, An Introduetion to Classieal Real Analysis
ENUMERATIVE COMBINATORICS VOL ME I RICHARD P. STANLEY
Wadsworth & Brooks/Cole Advanced Books & Software Monterey, California
Wadsworth & Brooks/Cole Advanced Books & Software
A Division of Wadsworth, Inc. ~)
1986 by Wadsworth, Inc., Belmont, California 94002. All rights reserved. No part of this
Sollcover reprint oCthe hardcover 1st edition 1986
book may be reproduced, stored in a retrieval system, or transcribed, in any form or by any means-electronic, mechanical, photocopying, recording, or otherwise-~without the prior written permission of the publisher, Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, California 93940, a division of Wadsworth, Inc. 10 9 8 7 6 5 4 3 2 1 Library of Congress Cataloging-in-Publication Data
Stanley, Richard P., [date] Enumerative combinatorics. Includes indexes. 1. Combinatorial enumeration problems. I. Title. QAI64.8.S73 1986 511'.62 86-14 ISBN 978-1-4615-9765-0 ISBN 978-1-4615-9763-6 (eBook) DOI 10.1007/978-1-4615-9763-6
Sponsoring Editor: lohn Kimmel Editorial Assistant: Maria Rosilio Alsadi Production Editor: Phyllis Larimore Production Assistant: Dorothy Bell M anuscript Editor: Gay Orr Art Coordinator: Lisa Torri Interior Illustration: Lori Heckeiman Typesetting: Asco Trade Typesetting Limited, Hong Kong Printing and Binding: Maple-Vail Book Manufacturing Group, York, Pennsylvania
Foreword
It is regrettable that a book, once published and on the way to starting a life of its own, can no longer bear witness to the painful choices that the author had to face in the course of his writing. There are choices that confront the writer of every book: who is the intended audience? who is to be proved wrong? who will be the most likely critic? Most of us have indulged in the idle practice of drafting tables of contents of books we know will never see the light of day. In some countries, some such particularly imaginative drafts have actually been sent to press (though they may not be included among the auth
