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Difference-covers that are not k-sum-covers. I

Published online by Cambridge University Press:  24 October 2008

T. H. Jackson ,
J. H. Williamson  and
D. R. Woodall
T. H. Jackson
Affiliation:
University of York, University of York and University of Nottingham
J. H. Williamson
Affiliation:
University of York, University of York and University of Nottingham
D. R. Woodall
Affiliation:
University of York, University of York and University of Nottingham
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Abstract

Various constructions are described for sets F = F(q, k, l) of residues modulo q such that F–F contains all residues while (k)F = F + F + … + F (k summands) omits l consecutive residues, in the cases k = 2, 3, 4 and 5. Let Q(k, l) denote the set of moduli q for which such a set F(q, k, l) exists. The following results are proved: q∈Q (2, 1) if and only if q ≥ 6; q∈Q(2,l) if q ≥ 4l + 2; 29, 31 and 33∈Q(3, 1) and if q∈Q(3, 1) if q ≥ 35; 24l + 21∈Q(3, l) if q ≥ 44l + 41. Upper bounds are also obtained for the least elements in Q(4, l) and Q(5, l).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 3 , November 1972 , pp. 425 - 438
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

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