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By V. G. Cerf, D. D. Cowan, R. C. Mullin, R. G. Stanton (auth.), Dr. Anne Penfold Street, Dr. Walter Denis Wallis (eds.)

ISBN-10: 3540071547

ISBN-13: 9783540071549

ISBN-10: 3540374825

ISBN-13: 9783540374824

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Read Online or Download Combinatorial Mathematics III: Proceedings of the Third Australian Conference Held at the University of Queensland, 16–18 May, 1974 PDF

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Extra info for Combinatorial Mathematics III: Proceedings of the Third Australian Conference Held at the University of Queensland, 16–18 May, 1974

Example text

If Withj = 0. quantity (-1)Jf(j) j:1 corresponding to the c h a r a c t e r x(J) is a d i v i s o r Let E odd r e s i d u e s . e(-1), q(1) of : defined by (-i) j det M = p V denote These and the set of even sets q(-1) are w e l l denote E(1) and X residues defined of since the c a r d i n a l i t y G and v of the = {j:j ¢ E; f(j) = 1} Z(-1) = {j:j ¢ E; f(j) = -1> Q(1) = {j:j c o; f(j) = 1} 0 the is even. sets , , , set of Let e(1), 37 Q(-1) = {j:j E o; f(j) = -1} respectively. Lemma prime, 5. we If £n a c y c l i c take a(1) ~ a(-1), then e(1) = (p2-1)/4, (i) e(-1) or (ii) p ~ 1 mod e(1) Proof, Since a(-1) which f a(1) Also there Hence not vanish q(1) and = (p-1)2/4 ; : (p2+p+2)/4, q(-1) = (p2-p)/4 ; and q(1) : (p2-p-2)/4, assume an odd = (p+1)2/4~ q(-1) = (p2+p)/4, we p and 4 = (p2-p)/2.

Third Manitoba Conference on Numerical Mathematics (1973), 379-398. Graph Theory (Addison-Wesley, [3] F. Harary, [4] A. J. Hoffman and R. R. , 1969) IBM Journal of Research and Development (1960), 497-504. A. Department of Computer University of Waterloo Science Ontario Canada Department of Combinatorics University of Waterloo and Optimization Ontario Canada Department of Computer University of Manitoba Science and Faculty of Mathematics University of Newcastle Winnipeg New South Wales Canada Australia A NOTE ON BALANCED WEIGHING MATRICES R, C, MULLIN A balanced w e i g h i n g m a t r i x is a square o r t h o g o n a l m a t r i x of l's and -l's O's, such that the m a t r i x obtained by squaring entries is the incidence m a t r i x of a (v, k, l) configuration.

D. Cowan, R. C. Mullin, Networks and Generalized Series R. G. Stanton, Moore Graphs, and (April, 1974). Computer Congressus Numerantium 9, Proc. Third Manitoba Conference on Numerical Mathematics (1973), 379-398. Graph Theory (Addison-Wesley, [3] F. Harary, [4] A. J. Hoffman and R. R. , 1969) IBM Journal of Research and Development (1960), 497-504. A. Department of Computer University of Waterloo Science Ontario Canada Department of Combinatorics University of Waterloo and Optimization Ontario Canada Department of Computer University of Manitoba Science and Faculty of Mathematics University of Newcastle Winnipeg New South Wales Canada Australia A NOTE ON BALANCED WEIGHING MATRICES R, C, MULLIN A balanced w e i g h i n g m a t r i x is a square o r t h o g o n a l m a t r i x of l's and -l's O's, such that the m a t r i x obtained by squaring entries is the incidence m a t r i x of a (v, k, l) configuration.

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Combinatorial Mathematics III: Proceedings of the Third Australian Conference Held at the University of Queensland, 16–18 May, 1974 by V. G. Cerf, D. D. Cowan, R. C. Mullin, R. G. Stanton (auth.), Dr. Anne Penfold Street, Dr. Walter Denis Wallis (eds.)


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