  We introduce and compare three different Monte Carlo determinantal algorithms
that allow one to compute dynamical quantities, such as the self-energy, of
fermionic systems in their thermodynamic limit. We show that the most efficient
approach expresses the sum of a factorial number of one-particle-irreducible
diagrams as a recursive sum of determinants with exponential complexity. By
comparing results for the two-dimensional Hubbard model with those obtained
from state-of-the-art diagrammatic Monte Carlo, we show that we can reach
higher perturbation orders and greater accuracy for the same computational
effort.
