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Feb 6 at 0:50 comment added Zach H You can derive the Stanley symmetric function result from Monk's rule, but I'm not aware of a purely geometric exposition. The toric Schur example is from 'Positroid varieties: juggling and geometry' by Knutson, Lam, and Speyer. The $k$-Schur example comes from work of Thomas Lam on affine Stanley symmetric functions. Another example is June Huh's proof for positivity of Chern-Schwartz-MacPherson classes.
Feb 5 at 19:12 comment added Chris McDaniel Sorry I know this was a while ago, but can you cite specific sources that use this technique?
Jun 19, 2017 at 20:41 history answered Zach H CC BY-SA 3.0