The Disjoint $m$-Flower Intersection Problem for Latin Squares

Abstract

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.