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We review the relation of N=4 superconformal multi-particle models on thereal line to the WDVV equation and an associated linear equation for twoprepotentials, F and U. The superspace treatment gives another variant of theintegrability problem, which we also reformulate as a search for closed flatYang-Mills connections. Three- and four-particle solutions are presented. Thecovector ansatz turns the WDVV equation into an algebraic condition, for whichwe give a formulation in terms of partial isometries. Three ideas forclassifying WDVV solutions are developed: ortho-polytopes, hypergraphs, andmatroids. Various examples and counterexamples are displayed.

N=4 Multi-Particle Mechanics, WDVV Equation and Roots