Recursive method for n -point tree-level amplitudes in supersymmetric Yang-Mills theories

We present a recursive method for super Yang-Mills color-ordered n-point tree amplitudes based on the cohomology of pure spinor superspace in ten space-time dimensions. The amplitudes are organized into BRST covariant building blocks with diagrammatic interpretation. Manifestly cyclic expressions (no longer than one line each) are explicitly given up to $n=10$ and higher leg generalizations are straightforward.