Combinatorics: Room Squares, Sum-Free Sets, Hadamard Matrices
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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
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improved
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Abbott,
Professor
help
encouragement.
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reading
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and
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We Professor of Part
who
unpublished
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to
thank
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of Part
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late
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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
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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
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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.
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authors
criticising
some
R.G.
G.
Dr.
Baumert,
for
those
and
tribute
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Mrs.
Roslyn
Mrs.
Abraham
Mills was
and and
ill.
to Mrs.
Karen
correcting Miss
Anne
many
Abraham
for
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splendid
inconsistencies.
Nicholls
for
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typing
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PART
1
PRELIMINARIES
-
3
-
CONTENTS
CHAPTER I.
INTRODUCTION
CHAPTER II.
BASIC DEFINITIONS
2.1
ARITHMETIC.
Galois Fields, Quadratic Numbers, Legendre
Symbol, Fez~nat Numbersp Cyclotomic Numbers 2.2
BALANCED INCOMPLETE BLOCK DESIGNS.
BIBD, (b,v,r,k,l)-
12
configurations, SBIBD, (v,k,l)-configurations 2.3
MATRICES.
Incidence Matrices, Hadamard Ma
