The disjoint m-flower intersection problem

An m-flower in a latin square is a set of m entries which share either a common row, a common column, or a common symbol, but which are otherwise distinct. Two m-flowers are disjoint if they share no common row, column or entry. In this paper we give a solution of the intersection problem for disjoint m-flowers in latin squares; that is, we determine precisely for which triples (n,m, x) there exists a pair of latin squares of order n whose intersection consists exactly of x disjoint m-flowers.