A generalization of plexes of Latin squares

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. We introduce the concept of a k -weight, an integral weight function on the cells of a Latin square whose row, column, and symbol sums are all k . We then show that several non-existence results about k -plexes can been seen as more general facts about k -weights and that the weight analogues of several well-known existence conjectures for plexes actually hold for k -weights.