J Austral Math Soc Ser A 43 pp257--267, 1987.

The Hadamard Conjecture and Integer Lattices

J. McCall and C. H. C. Little

(Received 20 January 1985; revised 25 August 1986)

Abstract

Let L be an integer lattice, and S be a set of lattice points of 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.

1980 AMS Subject Classification: 05B20

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Authors

J. McCall
C. H. C. Little: Department of Mathematics and Statistics, Massey University, Palmerston North, New Zealand.

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Last Modified: Wed Feb 26 16:48:07 2003