Proving stability numbers match for double Grothendieck and Schubert polynomials, suggesting deeper polynomial relationships.
We prove that products of double Grothendieck polynomials have the same back- and forward-stability numbers as products of Schubert polynomials, characterize which simple reflections appear in such products, and also give a new proof of a finiteness conjecture of Lam–Lee–Shimozono on products of back-stable Grothendieck polynomials, which was first proved by Anderson. To do this, we use the main theorems from our recent work, as well as expansion formulas of Lenart, Fomin–Kirillov, and Lam–Lee–Shimozono.
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Hardt et al. (2025) studied this question.
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