Terminology for f(g(x)) = g(f(x)) There is a paper by Ritt from 1923 that calls the relation,  $f(g(x)) = g(f(x))$, permutable functions. Is there a more recent terminology used in the literature, or is this still the standard?
It's common to say that $f$ and $g$ commute with respect to composition (where the property is known as commutativity). See, e.g., http://en.wikipedia.org/wiki/Function_composition.