  It is known that the Schur expansion of a skew Schur function runs over the
interval of partitions, equipped with dominance order, defined by the least and
the most dominant Littlewood-Richardson filling of the skew shape. We
characterise skew Schur functions (and therefore the product of two Schur
functions) which are multiplicity-free and the resulting Schur expansion runs
over the whole interval of partitions, i.e. skew Schur functions having
Littlewood-Richardson coefficients always equal to $1$ over the full interval.
