Combinatorics: Room Squares, Sum-free Sets, Hadamard Matrices

Lecture Notes in Mathematics A collection of informal reports and seminars Edited by A. Dold, Heidelberg and B. Eckmann, Z(Jrich 292 W. D. Wallis Anne Penfold Street Jennifer Seberry Wallis Combinatorics: Room Squares, Sum-Free Sets, Hadamard Matrices Springer-Verlag Berlin-Heidelberg • New York 1972 W. D. Wallis University of Newcastle, N. S. W., 2308/Australia Anne Penfold Street University of Queensland, St. Lucia, Queensland, 406?/Australia Jennifer Seberry Wallis University of Newcastle, N. S. W., 2308/Australia A M S Subject Classifications (1970): 05-02, 05 B 05, 05 B 10, 05 B 15, 05 B 20, 05 B 30, 05 C 15, 05 C20, 05 C25, 05 C 99,10 LOS, lOLlO, 12C20, 15 A 2 1 , 2 0 B 2 5 , 2 2 D 9 9 , 2 0 K 9 9 , 6 2 K 10 I S B N 3-540-06035-9 Springer-Verlag Berlin • H e i d e l b e r g • N e w Y o r k I S B N 0-387-06035-9 Springer-Verlag N e w Y o r k " H e i d e l b e r g • Berlin This work is subject to copyright. All rights are. reserved, whether the whole or part of the material is concerned, specifically those of translation~ reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a tee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin - Heidelberg 1972. Library of Congress Catalog Card Number 72~90443. Printed in Germany: Offsetdruck: Julius Beltz, Hemsbach/Bergstr. ACKNOWLEDGEMENTS We w i s h their has results, notes stimulated We Professor to t h a n k and on t h e i r improved especially H.L. wish Abbott, Professor help encouragement. and reading and and improving We Professor of Part who unpublished our to thank E.G. Szekeres the wish of Part Academic Stanton late sent us p r e p r i n t s and w h o s e The Press, Inc., K.R. A.L. to t h a n k 3 and remaining for p e r m i s s i o n Professor Mr. Professor also 4. work Whitehead, and much of Part have of correspondence work. We thank Moser, Matthews, Dr. Whiteman for Dr. Sheila Oates Dr. Baumert errors Professor to use Leo are J.G. our for L.D. their Macdonald reading own. Kalbfleisch the r e s u l t s and of c h a p t e r VIII 3. We p a y effort authors criticising some R.G. G. Dr. Baumert, for those and tribute finding Mrs. Roslyn Mrs. Abraham Mills was and and ill. to Mrs. Karen correcting Miss Anne many Abraham for her splendid inconsistencies. Nicholls for coming typing We a l s o to our r e s c u e thank when --t -r" -r'l '-,"t -...t ._J r'~ 4~ --I c.~ -...I f'D "~ -h o rn I