Abstract
A set {A 1, A 2,..., A t } of rectangular arrays, each defined on a symbol set X, is said to be t-perpendicular if each t-element subset of X occurs precisely once when the arrays are superimposed. We investigate the existence of sets of r by s rectangular arrays which are row-Latin, column-Latin and t-perpendicular. For example, we show that for all odd n, there exists a pair of row- and column-Latin 2-perpendicular r by s arrays with symbol set X of size n if and only if \(rs=\binom {n}{2}\) and r, s ≤ n.
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References
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Brier, R., Bryant, D. Perpendicular Rectangular Latin Arrays. Graphs and Combinatorics 25, 15–25 (2009). https://doi.org/10.1007/s00373-008-0822-8
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DOI: https://doi.org/10.1007/s00373-008-0822-8