We now consider some examples of jump systems. Example 1. Let M be a matroid over a set S, |S| = n. We let each coordinate of Z correspond to an element of S, and let J ⊆ {0, 1}n be the set of characteristic functions for bases of M , J = {χB|B a basis of M}. Claim 1. The set J is a jump system. Proof. Let x and y be the respective characteristic vectors of two bases b1 and b2 of M . A step x f...