One special case which I know about are the Boolean symmetric functions, introduced by L. Billera, S. Billey, and V. Tewari. They prove Schur positivity by using Chern plethysm, which I do not know much about. It is still open to to explain combinatorially the coefficients of the Schur expansion of the boolean symmetric functions.

A similar case which I know about are the Boolean symmetric functions, introduced by L. Billera, S. Billey, and V. Tewari. They prove Schur positivity by using Chern plethysm, which I do not know much about. It is still open to to explain combinatorially the coefficients of the Schur expansion of the boolean symmetric functions.