Completing partial latin squares with prescribed diagonals Original Research Article

This paper deals with completion of partial latin squares L=(lij) of order n with k cyclically generated diagonals (li+t,j+t=lij+t if lij is not empty; with calculations modulo n). There is special emphasis on cyclic completion. Here, we present results for k=2,…,7 and odd n⩽21, and we describe the computational method used (hill climbing). Noncyclic completion is investigated in the cases k=2,3 or 4 and n⩽21.