The University of Michigan Combinatorics Seminar


Abstract 

The totally nonnegative part of a real Grassmannian, denoted Gr_{k,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 Gr_{k,n}^{≥0}(R) is isomorphic (as a graded poset) to the poset
of decorated permutations, and the poset of Ldiagrams (certain tableau).
Additionally, the poset of cells of Gr_{k,n}^{≥0}(R) contains the Bruhat order
of the symmetric group S_{k}.
