I've read conjectures concerning the positivity of certain symmetric polynomials, which ask if a symmetric polynomial has all nonnegative coefficients when written in some basis. I'm curious what these mean combinatorially for the following bases:
m basis: monomial symmetric functions
e basis: elementary symmetric functions
p basis: power sum symmetric functions
s basis: Schur functions
For example, it is clear how to interpret the statement that the chromatic symmetric function is m-positive, but how would one interpret some of them being, say, e-positive?