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The number of non-homogeneous lattice points in n-dimensional point sets

Published online by Cambridge University Press:  24 October 2008

D. B. Sawyer
D. B. Sawyer
Affiliation:
University of OtagoDunedinNew Zealand
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Extract

Let R be a set of points in n-dimensional Euclidean space, and let Δ′(R) denote the lower bound of the determinants of non-homogeneous lattices which have no point in R. For Δ′(R) to be non-zero it is necessary, as Macbeath has shown (2), that R should have infinite volume.

Type
Research notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 1 , January 1953 , pp. 156 - 157
Copyright
Copyright © Cambridge Philosophical Society 1953

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References

REFERENCES

(1)Chaik, J. H. H.Quart. J. Math. 18 (1947), 216.Google Scholar
(2)Macbeath, A. M.Proc. Camb. phil. Soc. 47 (1951), 627–8.Google Scholar
(3)Rogers, C. A.J. Lond. math. Soc. 26 (1951), 308.Google Scholar