Doubly diagonal orthogonal latin squares |
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| Authors: | Katherine Heinrich AJW Hilton |
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| Institution: | Department of Mathematics, Simon Fraser University, Bumaby, B.C. V5A 1S6, Canada;Department of Mathematics, The University of Reading, Whiteknights, Reading RG6 2AX, England, UK |
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| Abstract: | A pair of doubly diagonal orthogonal latin squares of order n, DDOLS(n), is a pair of orthogonal latin squares of order n with the property that each square has a transversal on both the front diagonal (the cells {(i, i):1?i?n}) and the back diagonal (the cells {(i, n + 1?i): 1?i?n}). We show that for all n except n = 2, 3, 6, 10, 12, 14, 15, 18 and 26, there exists a pair of DDOLS(n). Obbviously these do not exist when n = 2, 3 and 6. |
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