Positroids and Schubert matroids

Recently Postnikov gave a combinatorial description of the cells in a totallynonnegative Grassmannian. These cells correspond to a special class of matroids called positroids. We prove his conjecture that a positroid is exactly an intersection of permuted Schubert matroids. This leads to a combinatorial description of positroids that is easily computable. The main proof is purely combinatorial, using only the characteristics of a Grassmann necklace and 3-term Plücker relations. The proof allows us to define positroids in terms of certain forbidden minors.