  There is considerable current interest in determining when the difference of
two skew Schur functions is Schur positive. We consider the posets that result
from ordering skew diagrams according to Schur positivity, before focussing on
the convex subposets corresponding to ribbons. While the general solution for
ribbon Schur functions seems out of reach at present, we determine necessary
and sufficient conditions for multiplicity-free ribbons, i.e. those whose
expansion as a linear combination of Schur functions has all coefficients
either zero or one. In particular, we show that the poset that results from
ordering such ribbons according to Schur-positivity is essentially a product of
two chains.
