Abstract. Norton and Stein associated a number with each idempotent quasigroup or diagonalized Latin square of given finite order n, showing that it is congruent mod 2 to the tria...
A k-plex of a latin square is a collection of cells representing each row, column, and symbol precisely k times. The classic case of k = 1 is more commonly known as a transversal....
A critical set in a latin square is a set of entries in a latin square which can be embedded in only one latin square. Also, if any element of the critical set is deleted, the rema...
In this paper, we consider the following question: what is the maximum number of entries that can be added to a partially lled latin square? The decision version of this question ...