Enumeration of totally positive Grassmann cells
Lauren K. Williams
MIT
February 13,
4:15pm
refreshments at 3:45pm
2338
ABSTRACT

Alex Postnikov recently gave a combinatorially explicit cell
decomposition of the totally nonnegative part of a Grassmannian, denoted
Gr_{kn}+, and showed that this set of cells is isomorphic as a graded
poset to many other interesting graded posets. The main result of our
work is an explicit generating function which enumerates the cells in
Gr_{kn}+ according to their dimension. As a corollary, we give a new
proof that the Euler characteristic of Gr_{kn}+ is 1. Additionally, we
use our result to produce a new qanalog of the Eulerian numbers, which
interpolates between the Eulerian numbers, the Narayana numbers, and the
binomial coefficients.

Speaker's Contact Info: lauren(atsign)math.mit.edu
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