  The U=infinity Hubbard model on a hypercubic lattice with exactly one hole is
studied. It is seen that a degeneracy can occur in the maximal-spin sector. It
is proved variationally that the Nagaoka (maximal spin) state is not a ground
state, if degeneracy exists. We give an explicit construction of a variational
state, an incommensurate spin-wave state, with energy lower than that of the
Nagaoka state. For the case of more than one hole, a few examples are discussed
where a degeneracy exists.
