  The fermionic Tonks-Girardeau (FTG) gas is a one-dimensional spin-polarized
Fermi gas with infinitely strong attractive zero-range odd-wave interactions,
arising from a confinement-induced resonance reachable via a three-dimensional
p-wave Feshbach resonance. We investigate the off-diagonal long-range order
(ODLRO) of the FTG gas subjected to a longitudinal harmonic confinement by
analyzing the two-particle reduced density matrix for which we derive a
closed-form expression. Using a variational approach and numerical
diagonalization we find that the largest eigenvalue of the two-body density
matrix is of order N/2, where N is the total particle number, and hence a
partial ODLRO is present for a FTG gas in the trap.
