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Integer difference covers which are not k-sum covers, for k = 6, 7

Published online by Cambridge University Press:  24 October 2008

Dennis Connolly
Dennis Connolly
Affiliation:
University of Lethbridge, Alberta, Canada
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Extract

Constructions are given of sets F(k), (k = 6, 7) of residues mod q(k), (for a suitably chosen integer q(k)) such that F(k) – F(k) contains all residues, while

has a gap of an assigned number of consecutive residues.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 1 , July 1973 , pp. 17 - 28
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

(1)Jackson, T. H., Williamson, J. H. and Woodall, D. R.Difference-covers that are not k-sum covers I. Proc. Cambridge Philos. Soc. 72 (1972), 425.Google Scholar
(2)Jackson, T. H. Asymmetric sets of residues, to appear. Mathematika.Google Scholar
(3)Williamson, J. H.Raikov systems. Symposia on theoretical physics and mathematics, vol. 8, pp. 173–183 (New York, 1968).Google Scholar
(4)Connolly, D. M. and Williamson, J. H.Difference-covers that are not k-sum-covers II, to appear.Google Scholar