We express connected Fermionic Green's functions in terms of two total
ly explicit tree formulas. The simplest and most symmetric formula, th
e Brydges-Kennedy formula is compatible with Gram's inequality. The se
cond one, the rooted formula of Abdesselam and Rivasseau, respects eve
n better the antisymmetric structure of determinants, and allows the d
irect comparison of rows and columns which correspond to the mathemati
cal implementation in Grassmann integrals of the Pauli principle. To i
llustrate the power of these formulas, we give a 'three lines proof' t
hat the radius of convergence of the Gross-Neveu theory with cutoff is
independent of the number of colors, using either one or the other of
these formulas.