  We investigate the scaling of the R\'{e}nyi entanglement entropies for a
particle bipartition of interacting spinless fermions in one spatial dimension.
In the Tomonaga-Luttinger liquid regime, we calculate the second R\'{e}nyi
entanglement entropy and show that the leading order finite-size scaling is
equal to a universal logarithm of the system size plus a non-universal
constant. Higher-order corrections decay as power-laws in the system size with
exponents that depend only on the Luttinger parameter. We confirm the
universality of our results by investigating the one dimensional $t-V$ model of
interacting spinless fermions via exact-diagonalization techniques. The
resulting sensitivity of the particle partition entanglement to boundary
conditions and statistics supports its utility as a probe of quantum liquids.
