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Orthogonal diagonal latin squares of order fourteen

Part of: Designs and configurations

Published online by Cambridge University Press:  09 April 2009

L. Zhu
L. Zhu
Affiliation:
Department of Mathematics Kiangsu Teachers CollegeSoochow, China
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Abstract

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Orthogonal diagonal latin squares of order n, ODLS(n), are orthogonal latin squares of order n with transversals on both the main diagonal and the back diagonal of each square. It has been proven that ODLS(n) exist for all n except n = 2, 3, 6, 10, 14, 15, 18 and 26, in which the first three are impossible. In this note an example of ODLS(14) is given.

MSC classification

Secondary: 05B15: Orthogonal arrays, Latin squares, Room squares
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 36 , Issue 1 , February 1984 , pp. 1 - 3
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Denes, J. and Keedwell, A. D., Latin squares and their applications (Academic Press, New York, 1974).Google Scholar
[2]Heinnch, K. and Hilton, A. J. W., ‘Doubly diagonal orthogonal latin squares’, to appear.Google Scholar
[3]Wallis, W. D. and Zhu, L., ‘Existence of orthogonal diagonal latin squares,’ Ars Combinatoria 12 (1981), 51–68.Google Scholar
[4]Wallis, W. D. and Zhu, L., ‘Some new orthogonal diagonal latin squares’, J. A ustral. Math. Soc. Ser. A, to appear.Google Scholar
[5]Wailis, W. D. and Zhu, L., ‘Four pairwise orthogonal diagonal latin squares of order 12,’ Utilitas Math. 21 C (1982), 205–207.Google Scholar