  We theoretically investigate in-medium two- and three-body correlations in
one-dimensional spinless fermions with attractive two-body p-wave interaction.
By investigating the variational problem of two- and three-body states above
the Fermi sea, we elucidate the fate of the in-medium two- and three-body
cluster states. The one-dimensional system with the strong p-wave interaction
is found to be stable against the formation of three-body clusters even in the
presence of the Fermi sea, in contrast to higher-dimensional systems that
suffer the strong three-body loss associated with the trimer formation.
