Under GRH and the Miltersen-Vinodchandran assumption, the positivity of Schubert coefficients has a positive rule, equivalent to the problem being in NP.
Buch, Frank Sottile and Alexander Yong, Quiver coefficients are Schubert structure constants, Math.\ Res.\ Lett
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Positivity of Schubert Coefficients
Under GRH and the Miltersen-Vinodchandran assumption, the positivity of Schubert coefficients has a positive rule, equivalent to the problem being in NP.