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Some Results on Configurations

Published online by Cambridge University Press:  09 April 2009

Jennifer Wallis
Affiliation:
University of NewcastleNew South Wales 2308
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A (v, k, λ) configurations is conjectured to exist for every v, k and λ satisfying λ(v − 1) = k(k − 1) and k − λ is a square if v is even, x2 = (k − λ)y2 + (−1)(v−1)/2 λz2 has a solution in integers x, y and z not all zero for v odd.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Ahrens, R. and Szekeres, G., ‘On a combinatorial generalization of 27 lines associated with a cubic surface’, J. Australian Math. Soc. 10 (1969), 485492.CrossRefGoogle Scholar
[2]Fisher, R. A. and Yates, F., Statistiol Tables for Biological, Agricultural, and Medical Research, 2nd ed. (Oliver and Boyd Ltd., London, 1943).Google Scholar
[3]Hall, Marshall Jr, Combinatorial Theory (Blaisdell, Waltham, Mass, 1967).Google Scholar
[4]Rao, C. Radhaskrishna, ‘A study of BIB designs with replications 11 to 15’, Sankhyā, 23 (1961) 117127.Google Scholar
[5]Ryser, H. J., Combinatorial Mathematics (Carus Monograph No. 14, Wiley, New York, 1963).CrossRefGoogle Scholar
[6]Sprott, D. A., ‘Listing of BIB designs from r = 16 to 20’, Sankhyā, Series A, 24 (1962), 203204.Google Scholar
[7]Takeuchi, K., ‘On the construction of a series of BIB designs’, Rep. Stat. Appl. Res., JUSE 10 (1963). 48.Google Scholar
[8]Wallis, Jennifer, ‘Some (1, –1) matrices’, J. Combinatorial Theory, (to appear).Google Scholar