Hybrid generic pipe dreams give a hybridization-independent equivariant formula for the classes of lower-upper varieties, proved via Yang-Baxter equations and a degeneration into complete intersections.
Bijective Proofs of Monk's rule for Schubert and Double Schubert Polynomials with Bumpless Pipe Dreams
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abstract
We give bijective proofs of Monk's rule for Schubert and double Schubert polynomials computed with bumpless pipe dreams. In particular, they specialize to bijective proofs of transition and cotransition formulas of Schubert and double Schubert polynomials, which can be used to establish bijections with ordinary pipe dreams.
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Hybrid pipe dreams for the lower-upper scheme
Hybrid generic pipe dreams give a hybridization-independent equivariant formula for the classes of lower-upper varieties, proved via Yang-Baxter equations and a degeneration into complete intersections.