On trades: an update Original Research Article

A pair of disjoint collections of k-subsets of a v-set X, {T1,T2}, is called a t-(v,k) trade if every t-subset of X appears precisely the same number of times in T1 as in T2. The purpose of this paper is to discuss the structures and properties of these combinatorial objects, review some of their applications, and present an update on the subject.