Completing partial latin squares with prescribed diagonals

Abstract

This paper deals with completion of partial latin squares L=( l ij ) of order n with k cyclically generated diagonals ( l i+ t, j+ t = l ij + t if l ij 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.