  We define an equivalence relation on integer compositions and show that two
ribbon Schur functions are identical if and only if their defining compositions
are equivalent in this sense. This equivalence is completely determined by
means of a factorization for compositions: equivalent compositions have
factorizations that differ only by reversing some of the terms. As an
application, we can derive identities on certain Littlewood-Richardson
coefficients. Finally, we consider the cone of symmetric functions having a
nonnnegative representation in terms of the fundamental quasisymmetric basis.
We show the Schur functions are among the extremes of this cone and conjecture
its facets are in bijection with the equivalence classes of compositions.

Combinatorics