  We study the zero-energy collision of three identical spin-polarized fermions
with short-range interactions in one dimension. We derive the asymptotic
expansions of the three-body wave function when the three fermions are far
apart or one pair and the third fermion are far apart, and the three-body
scattering hypervolume $D_F$ appears in the coefficients of such expansions. If
the two-body interaction is attractive and supports two-body bound states,
$D_F$ acquires a negative imaginary part related to the amplitudes of the
outgoing waves describing the departure of the resultant bound pair and the
remaining free fermion. For weak interaction potentials, we derive an
approximate formula of the hypervolume by using the Born expansion. For the
square-barrier and the square-well potentials and the Gaussian potential, we
solve the three-body Schr\"{o}dinger equation to compute $D_F$ numerically. We
also calculate the shifts of energy and of pressure of spin-polarized
one-dimensional Fermi gases due to a nonzero $D_F$ and the three-body
recombination rate in one dimension.
