Mészáros–Setiabrata–St. Dizier interval-support conjecture for Grothendieck polynomials

Let SnS_n be the symmetric group, let ωSn\omega\in S_n, and let p1(x1,,xn)p_1(x_1,\ldots,x_n) and p2(x1,,xn)p_2(x_1,\ldots,x_n) be monomials with nonzero coefficient in the Grothendieck polynomial Gω\mathfrak{G}_{\omega} such that p1p_1 divides p2p_2. Mészáros–Setiabrata–St. Dizier's interval-support conjecture. Every monomial q(x1,,xn)q(x_1,\ldots,x_n) satisfying p1qp_1\mid q and qp2q\mid p_2 also has nonzero coefficient in Gω\mathfrak{G}_{\omega}. This predicts that the support of each Grothendieck polynomial is order-convex under divisibility; the source presents it as a conjecture about support, with no resolution supplied.

Sources & referencesView supporting material

Primary source

Elena S. Hafner, “Vexillary Grothendieck Polynomials via Bumpless Pipe Dreams”, arXiv:2201.12432 (2022).

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