An intersection theorem for supermatroids

Abstract We generalize the matroid intersection theorem to distributive supermatroids, a structure that extends the matroid to the partially ordered ground set. Distributive supermatroids are special cases of both supermatroids and greedoids, and they generalize polymatroids. This is the first good characterization proved for the intersection problem of an independence system where the ground set is partially ordered. The characterization given has a more complex structure than the matroid (or polymatroid) intersection theorem.