  The two-dimensional one-component plasma ---2dOCP--- is a system composed by
$n$ mobile particles with charge $q$ over a neutralizing background in a
two-dimensional surface. The Boltzmann factor of this system, at temperature
$T$, takes the form of a Vandermonde determinant to the power $\Gamma =
q^2/(2\pi\varepsilon k_BT)$, where $\Gamma$ is the coupling constant of this
Coulomb system. The partition function of the model has been computed exactly
for the even values of the coupling constant $\Gamma$, and a finite number of
particles $n$, by two means: 1) by recognizing that the Boltzmann factor is the
square of a Jack polynomial and expanding it in an appropriate monomial base,
and 2) by mapping the system onto a 1-dimensional chain of interacting
fermions. In this work the connection among the two methods is derived, and
some properties of the expansion coefficients for the power of the Vandermonde
determinant are explored.
