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Arrays and brooks

Published online by Cambridge University Press:  09 April 2009

B. T. Bennett  and
R. B. Potts
B. T. Bennett
Affiliation:
Mathematics Department University of Adelaide
R. B. Potts
Affiliation:
Mathematics Department University of Adelaide
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Consider an m × n rectangular array whose m rows are permutations of 1, 2, …, n. Such an array will be called a constant-sum array if the sum of the elements in each column is the same (and equal to ½m (n+1)). An example of a 3×9 constant-sum array is In contrast to a Latin rectangle, elements in the same column of a constantsum array may be equal. It will be convenient to assume arrays normalised in the sense that the columns are arranged so that, as in (1), the first row is in the standard order 1, 2, …, n.

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 7 , Issue 1 , February 1967 , pp. 23 - 31
Copyright
Copyright © Australian Mathematical Society 1967

References

[1]Kraitchik, M., Mathematical Recreations (G. Allen and Unwin, 1943), Ch. 10.Google Scholar
[2]Riordan, J., An Introduction to Combinatorial Analysis (Wiley, 1958), Ch. 7, 8.Google Scholar
[3]Ledermann, W., Introduction to the Theory of Finite Groups (Oliver and Boyd, 1953), p. 89.Google Scholar