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The Hadamard conjecture and integer lattices

Part of: Designs and configurations

Published online by Cambridge University Press:  09 April 2009

J. McCall  and
C. H. C. Little
J. McCall
Affiliation:
Department of Mathematics and StatisticsMassey UniversityPalmerston North, New Zealand
C. H. C. Little
Affiliation:
Department of Mathematics and StatisticsMassey UniversityPalmerston North, New Zealand
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Abstract

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Let L be an integer lattice, and S a set of lattice points in L. We say that S is optimal if it minimises the number of rectangular sublattices of L (including degenerate ones) which contain an even number of points in S. We show that the resolution of the Hadamard conjecture is equivalent to the determination of |S| for an optimal set S in a (4s-1) × (4s-1) integer lattice L. We then specialise to the case of 1 × n integer lattices, characterising and enumerating their optimal sets.

MSC classification

Secondary: 05B20: Matrices (incidence, Hadamard, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 43 , Issue 2 , October 1987 , pp. 257 - 267
Copyright
Copyright © Australian Mathematical Society 1987

References

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