  Motivated by the spate of recent experimental and theoretical interest in
Mott insulating S=1 triangular lattice magnets, we consider a model S=1
Hamiltonian on a triangular lattice interacting with rotationally symmetric
biquadratic interactions. We show that the partition function of this model can
be expressed in terms of configurations of three colors of tightly-packed,
closed loops with {\em non-negative} weights, which allows for efficient
quantum Monte Carlo sampling on large lattices. We find the ground state has
spin nematic order, i.e. it spontaneously breaks spin rotation symmetry but
preserves time reversal symmetry. We present accurate results for the
parameters of the low energy field theory, as well as finite-temperature
thermodynamic functions.
