  A simple, combinatorial construction of the sl(n)-WZNW fusion ring, also
known as Verlinde algebra, is given. As a byproduct of the construction one
obtains an isomorphism between the fusion ring and a particular quotient of the
small quantum cohomology ring of the Grassmannian Gr(k,k+n). We explain how our
approach naturally fits into known combinatorial descriptions of the quantum
cohomology ring, by establishing what one could call a
`Boson-Fermion-correspondence' between the two rings. We also present new
recursion formulae for the structure constants of both rings, the fusion
coefficients and the Gromov-Witten invariants.
