The University of Michigan Combinatorics Seminar
The totally nonnegative part of a real Grassmannian, denoted Grk,n≥0(R), is
a certain CW complex contained in the Grassmannian which has some amazing
combinatorial properties. For example, Alex Postnikov has shown that the
poset of cells of Grk,n≥0(R) is isomorphic (as a graded poset) to the poset
of decorated permutations, and the poset of L-diagrams (certain tableau).
Additionally, the poset of cells of Grk,n≥0(R) contains the Bruhat order
of the symmetric group Sk.