  The canonical $\,NLT\,$ partition function of a quasi-one dimensional (q1D)
one-file system of equal hard disks [J. Chem Phys. \textbf{153}, 144111 (2020)]
provides an analytical description of the thermodynamics and ordering in this
system (a pore) as a function of linear density $\,Nd/L\,$ where $\,d\,$ is the
disk diameter. We derive the analytical formulae for the distance dependence of
the translational pair distribution function and the distribution function of
distances between next neighbor disks, and then demonstrate their use by
calculating the translational order in the pore. In all cases, the order is
found to be of a short range and to exponentially decay with the disks'
separation. The correlation length presented for different pore widths and
densities shows a non-monotonic dependence with a maximum at $\,Nd/L = 1\,$ and
tends to the 1D value for a vanishing pore width. The results indicate a
special role of this density when the pore length $\,L\,$ is equal exactly to
$N$ disk diameters. A comparison between the theoretical results for an
infinite system and the results of a molecular dynamics simulation for a finite
system with periodic boundary conditions is presented and discussed.
