Positroids and Schubert matroids

Abstract

Postnikov gave a combinatorial description of the cells in a totally-nonnegative Grassmannian. These cells correspond to a special class of matroids called positroid. We prove his conjecture that a positroid is exactly an intersection of permuted Schubert matroids. This leads to a nice combinatorial description of positroids that is easily computable.

10 pages, 1 figure. v5 simpler proof with improved writing. Submitted

References in corpus (1)

• Lattice path matroids: enumerative aspects and Tutte polynomials

Cited by in corpus (3)

• Positroid varieties I: juggling and geometry
• Toric Poisson Ideals in Cluster Algebras
• $\LE$-diagrams and totally positive bases inside the nonnegative Grassmannian