Abstract

AbstractA Latin array is a matrix of symbols in which no symbol occurs more than once within a row or within a column. A diagonal of an n × n array is a selection of cells taken from different rows and columns of the array. The weight of a diagonal is the number of different symbols on it. We show via computation that every Latin array of order has a diagonal of weight at least . A corollary is the existence of near transversals in Latin squares of these orders. More generally, for all we compute a lower bound on the order of any Latin array that does not have a diagonal of weight at least .

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