  We show that without other further assumption than affine equivariance and
locality, a numerical integrator has an expansion in a generalized form of
Butcher series (B-series) which we call aromatic B-series. We obtain an
explicit description of aromatic B-series in terms of elementary differentials
associated to aromatic trees, which are directed graphs generalizing trees. We
also define a new class of integrators, the class of aromatic Runge-Kutta
methods, that extends the class of Runge-Kutta methods, and have aromatic
B-series expansion but are not B-series methods. Finally, those results are
partially extended to the case of more general affine group equivariance.
