The Schur–Horn conjecture for homogeneous multiaffine polynomials

A homogeneous multiaffine polynomial is a polynomial in which every variable has degree at most one and all monomials have the same total degree. Multiaffine Schur–Horn conjecture. Every homogeneous multiaffine polynomial has the Schur–Horn property. The authors report that computer searches found no counterexample, but the general assertion is presented as an open conjecture.