On maximal premature partial Latin squares (Q2760457)

A partial Latin square is an \(n \times n\) array partially filled by numbers from \(\{1,2,\dots ,n\}\) such that every row and column contains each number at most once. A partial Latin square is premature if it cannot be completed to a Latin square, but such a completion exists after erasing the contents of any cell. In this paper, the author showed that the number of empty cells in an \(n \times n\) premature Latin square is at least \(7n/2 - o(n)\).