  We demonstrate that the sign structure of the t-J model on a hypercubic
lattice is entirely different from that of a Fermi gas, by inspecting the high
temperature expansion of the partition function up to all orders, as well as
the multi-hole propagator of the half-filled state and the perturbative
expansion of the ground state energy. We show that while the fermion signs can
be completely gauged away by a Marshall sign transformation at half-filling,
the bulk of the signs can be also gauged away in a doped case, leaving behind a
rarified "irreducible" sign structure that can be enumerated easily by counting
exchanges of holes with themselves and spins on their real space paths. Such a
sparse sign structure implies a mutual statistics for the quantum states of the
doped Mott insulator.
