  Being motivated by the surge of fermionic quantum Monte Carlo simulations at
finite temperature, we present a detailed analysis of the permutation-cycle
properties of path integral Monte Carlo (PIMC) simulations of degenerate
electrons. Particular emphasis is put onto the uniform electron gas in the warm
dense matter regime. We carry out PIMC simulations of up to $N=100$ electrons
and investigate exchange-cycle frequencies, which are found not to follow any
simple exponential law even in the case of ideal fermions due to the finite
size of the simulation box. Moreover, we introduce a permutation-cycle
correlation function, which allows us to analyse the joint probability to
simultaneously find cycles of different lengths within a single configuration.
Again, we find that finite-size effects predominate the observed behaviour.
Finally, we briefly consider an inhomogeneous system, namely electrons in a
$2D$ harmonic trap. We expect our results to be of interest for the further
development of fermionic PIMC methods, in particular to alleviate the notorious
fermion sign problem.
