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Nonexistence of certain supplementary difference sets

Published online by Cambridge University Press:  17 April 2009

Nicholas Wormald
Nicholas Wormald
Affiliation:
Department of Pure Mathematics, Faculty of Arts, Australian National University, Canberra. ACT.
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Abstract

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This paper finds restrictions on the parameters of supplementary difference sets in any group G with a subgroup of index 2, which therefore includes all cyclic groups of even orders. As a corollary to the main theorem, we have that if S1, …, Sr are r − {2v, k1, …, kr; 2λ} supplementary difference sets in such a group, then not all of v, k1, …, kr, λ are odd; also is the sum of r squares.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 13 , Issue 3 , December 1975 , pp. 343 - 348
Copyright
Copyright © Australian Mathematical Society 1975

References

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[3]Wallis, Jennifer Seberry, “Some remarks on supplementary difference sets”, Infinite and finite sets, Vol. III, 1503–1526 (Colloquia Mathematica Societatis János Bolyai, 10. North-Holland, Amsterdam, London, 1975).Google Scholar