In the set theoretic axiomatization of an antimatroid there are certain special sets called paths that determine the whole antimatroid, in the sense that the sets of the antimatroid are exactly the unions of paths. If S is any feasible set of the antimatroid, an element x that can be removed from S to form another feasible set is called an endpoint of S, and a feasible set that has only one endpoint is called a path of the antimatroid. The family of paths can be partially ordered by set inclusion, forming the path poset of the antimatroid.
