  We theoretically investigate in-medium two- and three-body correlations in
one-dimensional two-component Fermi gases with coexistent even-parity s-wave
and odd-parity p-wave interactions. We find the solutions of the stable
in-medium three-body cluster states such as Cooper triple by solving the
corresponding in-medium variational equations. We further feature the phase
diagram consisting of the s- and p-wave Cooper pairing phase, and Cooper
tripling phase, in the plane of s- and p-wave pairing strengths. The Cooper
tripling phase dominates over the pairing phases when both s- and p-wave
interactions are moderately strong.
