Applications of Fibonacci Numbers Volume 8
This book contains 33 papers from among the 41 papers presented at the Eighth International Conference on Fibonacci Numbers and Their Applications which was held at the Rochester Institute of Technology, Rochester, New York, from June 22 to June 26, 1998.
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Applications of Fibonacci Numbers Volume 8 Proceedings of 'The Eighth International Research Conference on Fibonacci Numbers and Their Applications', Rochester Institute of Technology, Rochester, New York, U.S.A., June 22-26, 1998
edited by
Fredric T. Howard Department of Mathematics and Computer Science, Wake Forest University, Winston-Salem, North Carolina, U.S.A.
SPRINGER SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-94-010-5851-3 ISBN 978-94-011-4271-7 (eBook) DOI 10.1007/978-94-011-4271-7
Cover figure by John C. Turner
Printed on acid-free paper
All Rights Reserved
© 1999 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1999 Softcover reprint of the hardcover 1st edition 1999 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.
TABLE OF CONTENTS
A REPORT ON THE EIGHTH INTERNATIONAL CONFERENCE .................................... vii LIST OF CONTRIBUTORS TO THIS PROCEEDINGS ......................................................... ix FOREWORD ........................................................................................................................ xvii THE ORGANIZING COMMITTEES .................................................................................... xix LIST OF CONTRIBUTORS TO THE CONFERENCE ........................................................ xxi INTRODUCTION .............................................................................................................. xxiii ON THE GENERALIZED BINOMIAL COEFFICIENTS DEFINED BY STRONG DIVISIBILITY SEQUENCES Shiro Ando and Daihachiro Sato ................................................................................... l ON TRIANGLES AND SQUARES MARKED WITH GOLD POINTS-STUDIES OF GOLDEN TILES Vassia K. Anatassova and J.C. Turner....................................................................... 11 MULTIVARIATE PASCAL POLYNOMIALS OF ORDER K WITH PROBABILITY APPLICATIONS Demetrios L. Antzoulakos and Andreas N. Philippou ................................................. 27 FIBONACCI PLANES AND SPACES K.T. Atanassov and A.G. Shannon ............................................................................ 43 THE SMALLEST POSITIVE INTEGER HAVING Fk REPRESENTATIONS AS SUMS OF DISTINCT FIBONACCI NUMBERS Marjorie Bicknell-Johnson ......................................................................................... 47 THE ZECKENDORF-WYTHOFF ARRAY APPLIED TO COUNTING THE NUMBER OF REPRESENTATIONS OF N AS SUMS OF DISTINCT FIBONACCI NUMBERS Marjorie Bicknell-Johnson ......................................................................................... 53 COMPOSING WITH SEQUENCES: •.•BUT IS IT ART? John A. Biles ............................................................
