  We propose a novel way to describe numerical methods for ordinary
differential equations via the notion of multi-indice. The main idea is to
replace rooted trees in Butcher's B-series by multi-indices. The latter were
introduced recently in the context of describing solutions of singular
stochastic partial differential equations. The combinatorial shift away from
rooted trees allows for a compressed description of numerical schemes.
Moreover, these multi-indices B-series characterise uniquely the Taylor
development of local and affine equivariant maps.
