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The recursive method of Berends and Giele to compute tree-level gluonamplitudes is revisited using the framework of ten-dimensional superYang-Mills. First we prove that the pure spinor formula to compute SYM treeamplitudes derived in 2010 reduces to the standard Berends-Giele formula fromthe 80s when restricted to gluon amplitudes and additionally determine thefermionic completion. Second, using BRST cohomology manipulations insuperspace, alternative representations of the component amplitudes areexplored and the Bern-Carrasco-Johansson relations among partial treeamplitudes are derived in a novel way. Finally, it is shown how thesupersymmetric components of manifestly local BCJ-satisfying tree-levelnumerators can be computed in a recursive fashion.

Berends-Giele recursions and the BCJ duality in superspace and components