  We have studied the ground-state properties of para-hydrogen in one dimension
and in quasi-one-dimensional configurations using the path integral ground
state Monte Carlo method. This method produces zero-temperature exact results
for a given interaction and geometry. The quasi-one-dimensional setup has been
implemented in two forms: the inner channel inside a carbon nanotube coated
with H$_2$ and a harmonic confinement of variable strength. Our main result is
the dependence of the Luttinger parameter on the density within the stable
regime. Going from one dimension to quasi-one dimension, keeping the linear
density constant, produces a systematic increase of the Luttinger parameter.
This increase is however not enough to reach the superfluid regime and the
system always remain in the quasi-crystal regime, according to Luttinger liquid
theory.
