Perpendicular rectangular Latin arrays
A set \(\{A_1,A_2,\dots,A_t\}\) 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. The authors investigate the existence of sets of \(r \times s\) rectangular arrays which are row-Latin, column-Latin, and \(t\)-perpendicular. For example, they show that for all odd \(n\), there exists a pair of row- and column-Latin 2-perpendicular \(r \times s\) arrays with symbol set \(X\) of size \(n\) if and only if \(rs = \tbinom{n}{2}\) and \(r,s \leq n\). This is an interesting result in a paper that is nice to read.
scientific article; zbMATH DE number 5644625