Characterize toric g-polynomials of convex polytopes

Characterize the complete class of polynomials that occur as toric g-polynomials of convex polytopes.

Background

The paper establishes that Kazhdan–Lusztig polynomials of lattice Bruhat intervals coincide with toric g-polynomials of polytopes constructed from those intervals. This yields restrictions such as nonnegative coefficients, no internal zeros, multiplicative monotonicity, and generalized upper bounds. However, the authors emphasize that these restrictions do not provide a complete characterization of the possible toric g-polynomials of convex polytopes.