Abstract
A periodic binary array is said to besequential if and only if every line of the array is occupied by a given periodic binary sequence or by some cyclic shift or reversal of this sequence. This paper extends earlier results for arrays built on the square grid, characterising further sequential arrays with two ones per period, and those with three consecutive ones per period.
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References
Day, Robert andStreet, Anne Penfold,Sequential binary arrays I: the square grid. J. Comb. Theory, Ser. A32 (1982), 35–52.
Street, Anne Penfold andDay, Robert,Sequential binary arrays II: further results on the square grid. InComb. Math. IX, Proc. Ninth Aust. Conf., Lecture Notes in Math. No. 952, Springer, Berlin-Heidelberg-New York, 1982, pp. 392–418.
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Praeger, C.E., Street, A.P. Characterisation of some sparse binary sequential arrays. Aeq. Math. 26, 54–58 (1983). https://doi.org/10.1007/BF02189664
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DOI: https://doi.org/10.1007/BF02189664