Embedding an incomplete latin square in a latin square with a prescribed diagonal (Q796539)

Necessary and sufficient conditions are presented for the embedding of a given incomplete latin square R of size n, \(n\geq 10\) on the symbols \(\sigma_ 1,...,\sigma_ t\) in a latin square T of side t on the symbols \(\sigma_ 1,...,\sigma_ t\) for all \(t\geq 2n+1\) where the diagonal of T has been prescribed. The lower bound of \(2n+1\) for t is the best possible.