A signed tiling rule computes every Schubert coefficient, and the rule implies a new polynomiality result for coefficient sums with bounded inversions.
A Schubert calculus recurrence from the noncomplex W-action on G/B
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abstract
In this paper, as in our previous "Descent-cycling in Schubert calculus" math.CO/0009112, we study the structure constants in equivariant cohomology of flag manifolds G/B. In this one we give a recurrence (which is frequently, but alas not always, positive) to compute these one by one, using the non-complex action of the Weyl group on G/B. Probably the most noteworthy feature of this recurrence is that to compute a particular structure constant c_{lambda,mu}^nu, one does not have to compute the whole product S_lambda * S_mu.
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Signed puzzles for Schubert coefficients
A signed tiling rule computes every Schubert coefficient, and the rule implies a new polynomiality result for coefficient sums with bounded inversions.