The disjoint \(m\)-flower intersection problem for Latin squares (Q540015)

Summary: 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.