  We investigate the strong-coupling limit of a three-component Fermi mixture
in an optical lattice with attractive interactions. In this limit bound states
(trions) of the three components are formed. We derive an effective Hamiltonian
for these composite fermions and show that it is asymptotically equivalent to
an antiferromagnetic Ising model. By using Monte-Carlo simulations, we
investigate the spatial arrangement of the trions and the formation of a
trionic density wave (CDW), both in a homogeneous lattice and in the presence
of an additional harmonic confinement. Depending on the strength of the
confinement and on the temperature, we found several scenarios for the trionic
distribution, including coexistence of disordered trions with CDW and band
insulator phases. Our results show that, due to a proximity effect, staggered
density modulations are induced in regions of the trap where they would not
otherwise be present according to the local density approximation.
