DECOMPOSITION OF PARTIAL ORDERS

A decomposition theory for partial orders which arises from the split decomposition of submodular functions is introduced. As a consequence of this theory, any partial order has a unique decomposition consisting of indecomposable partial orders and certain highly decomposable partial orders. The highly decomposable partial orders are completely characterized. As a special case of partial orders, we consider lattices and distributive lattices. It occurs, that the highly decomposable distributive lattices are precisely the Boolean lattices. © 1990 Kluwer Academic Publishers.