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Another proof of a theorem on difference sets

Published online by Cambridge University Press:  24 October 2008

D. L. Yates
D. L. Yates
Affiliation:
University of Nottingham
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Extract

Multipliers of a difference set are of great importance in existence theorems, since they enable us to reject many configurations en bloc. (For a description of such theorems, see Mann (1).) The following theorem, which determines those cyclic group difference sets for which −1 is a multiplier, has been proved before by different methods (see, for example, Yamamoto(2) and Johnsen(3); and a more elementary matrix proof by Brualdi(4)) but the following ‘elementary’ proof may be of interest.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 3 , July 1967 , pp. 595 - 596
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Mann, H. B.Addition theorems, chapter 7 (Wiley, 1965).Google Scholar
(2)Yamamoto, K.Decomposition fields of difference sets. Pacific J. Math. 13 (1963), 337–352.CrossRefGoogle Scholar
(3)Johnsen, E. C.The inverse multiplier for Abelian group difference sets. Canadian J. Math. 16 (1964), 787–796.CrossRefGoogle Scholar
(4)Brualdi, R. A.A note on multipliers of difference sets. J. Res. Bur. Standards. 69B (1965), 87–89.CrossRefGoogle Scholar
(5)Halberstam, H. and Laxton, R. R.Perfect difference sets. Perfect difference sets 6, 4 (1964), 177–184.Google Scholar