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Sequential binary arrays and circulant matrices

Part of: Designs and configurations

Published online by Cambridge University Press:  09 April 2009

Cheryl E. Praeger  and
Chaufah K. Nilrat
Cheryl E. Praeger
Affiliation:
Department of MathematicsUniversity of Western AustraliaNedlands, W. A. 6009, Australia
Chaufah K. Nilrat
Affiliation:
Department of MathematicsFaculty of Science Prince of Songkla UniversityHaad Yai, Thailand
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Abstract

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A periodic binary array on the sequare grid is said to be sequential if and only if each row and each column of the array contains a given periodic binary sequence or some cyclic shift or reversal of this sequence. Such arrays are of interest in connection with experimental layouts. This paper extends previous results by characterizing sequential arrays on sequences of the type (1,…,1,0,…,0) and solving the problem of equivalence of such arrays (including a computation of the number of equivalence classes).

MSC classification

Secondary: 05B20: Matrices (incidence, Hadamard, etc.)

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 42 , Issue 3 , June 1987 , pp. 330 - 348
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Burnside, W., Theory of Groups of Finite Order (Cambridge University Press, Second edition 1911; reprinted Dover, London, 1955).Google Scholar
[2]Day, R. and Street, A. P., ‘Sequential binary arrays. I. The square grid’, J. Combinatorial Theory Ser. A 32 (1982), 35–52.CrossRefGoogle Scholar
[3]Macdonald, S. Oates and Street, A. P., ‘Balanced binary arrays. II. The triangular grid’, Ars Combinatoria 8 (1979), 65–84.Google Scholar
[4]Macdonald, S. Oates and Street, A. P., ‘Balanced binary arrays. III. The hexagonal grid’, J. Austral. Math. Soc. Ser. A 28 (1979), 479–498.Google Scholar
[5]Praeger, C. E. and Street, A. P., ‘Characterization of some sparse binary sequential arrays’, Aequationes Math. 26 (1983), 54–58.CrossRefGoogle Scholar
[6]Street, A. P. and Day, R., ‘Sequential binary arrays II: further results on the square grid’ (Combinatorial Mathematics IX, Lecture Notes in Math., Vol. 952, Springer-Verlag, Berlin, Heidelberg, New York, 1982), pp. 392–418.CrossRefGoogle Scholar
[7]Street, A. P. and Macdonald, S. Oates, ‘Balanced binary arrays. I. The square grid’ (Combinatorial Mathematics VI, Lecture Notes in Math., Vol. 748, Springer-Verlag, Berlin, Heidelberg, New York, 1979), pp. 165–198.CrossRefGoogle Scholar