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A theorem on cubes

Published online by Cambridge University Press:  26 February 2010

D. R. Woodall
D. R. Woodall
Affiliation:
Department of Mathematics, University of Nottingham, England, NG7 2RD.
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Summary

It is proved that, if R is a set of r vertices of an n–dimensional cube, then the number of distinct mid-points of line-segments joining pairs of points of R (including the points of R themselves as mid-points) is at least rx, where

This result is (in a sense) best possible.

Type
Research Article
Information
Mathematika , Volume 24 , Issue 1 , June 1977 , pp. 60 - 62
Copyright
Copyright © University College London 1977

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References

1.Brown, G. and Moran, W.. Problem posed at the L.M.S. Research Symposium on Functional Analysis and Stochastic Processes, Durham (England), August 1974.Google Scholar
2.Hall, R. R.. “A problem in combinatorial geometry”, J. London Math. Soc., (2), 12 (1976), 315–319.CrossRefGoogle Scholar