A (partial) system of distinct representatives is a set of distinct elements {x1,x2,…xk} such that xi∈Aji, where j1,j2,…,jk are distinct integers in [n]. I...A (partial) system of distinct representatives is a set of distinct elements {x1,x2,…xk} such that xi∈Aji, where j1,j2,…,jk are distinct integers in [n]. In standard usage, "system of distinct representatives'' means "complete system of distinct representatives'', but it will be convenient to let "system of distinct representatives'' mean either a complete or partial system of distinct representatives depending on context.
