Monical–Tokcan–Yong's saturated Newton polytope conjecture for double Schubert polynomials

At least 4 years old · documented by

Let Sp{\mathfrak{S}}_p be the symmetric group, and let Sπ(\normalfontt,\normalfonts){\mathfrak{S}}_\pi({\normalfont\mathbf{t}}, {\normalfont\mathbf{s}}) be the double Schubert polynomial associated to a permutation π∈Sp\pi\in{\mathfrak{S}}_p. For a polynomial f=∑\normalfontnc\normalfontn\normalfontx\normalfontnf=\sum_{\normalfont\mathbf{n}}c_{\normalfont\mathbf{n}}{\normalfont\mathbf{x}}^{\normalfont\mathbf{n}}, its Saturated Newton Polytope property means that its support equals the lattice points in its Newton polytope.

Saturated Newton polytope conjecture. Every double Schubert polynomial Sπ(\normalfontt,\normalfonts){\mathfrak{S}}_\pi({\normalfont\mathbf{t}}, {\normalfont\mathbf{s}}) has the Saturated Newton Polytope property.

The conjecture asserts that the monomial support of each double Schubert polynomial is exactly the set of integer points in its Newton polytope. The paper's stated goal is to confirm this conjecture, so it is solved in the source.

References

Primary source

Federico Castillo, Yairon Cid-Ruiz, Fatemeh Mohammadi and Jonathan Montaño, “Double Schubert polynomials do have saturated Newton polytopes”, arXiv:2109.10299 (2023).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.