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These notes are a written version of my talk given at the CARMA workshop inJune 2017, with some additional material. I presented a few concepts that haverecently been used in the computation of tree-level scattering amplitudes(mostly using pure spinor methods but not restricted to it) in a context thatcould be of interest to the combinatorics community. In particular, I focusedon the appearance of {\it planar binary trees} in scattering amplitudes andpresented some curious identities obeyed by related objects, some of which areknown to be true only via explicit examples.

Planar binary trees in scattering amplitudes