Comment on a Note by J. Marica and J. Schönheim

Abstract

In [2] it is shown that an n × n partial latin square with n — 1 cells occupied on the main diagonal can be completed to a latin square. We can use the technique in [2] to prove the following result.An n × n partial latin square with n — 1 cells occupied with n — 1 distinct symbols can be completed to a latin square if the occupied cells are in different rows or different columns.Let P be an n × n partial latin square based on 0,1, 2, …, n — 1 satisfying the above conditions, and let (x0, y0), (x1, y1), …, (xn-2, yn-2) De the occupied cells where y0, y1, … yn-2 are distinct.