@highergeometer @BrKloeckner @johncarlosbaez Perhaps this is related? https://www.math4wisdom.com/wiki/Exposition/20221122SpaceBuilders About partitions of sets, which are encoded by orthogonal #Sheffer polynomials (which come up in solutions of the #SchroedingerEquation ). There is a fivefold classification of these orthogonal Sheffer polynomials and they each have their own weight function (these are the natual exponential families with quadratic variance functions) which you can get from the moments.

I enjoyed Nima Arkani-Hamed's popular talk "The End of Space-Time" as a gentle context for me to understand the #amplituhedron I see parallels with the discrete model in my video "Combinatorial Interpretation of the #SchroedingerEquation " https://www.youtube.com/watch?v=6ReRg_TCKSY where integrals are replaced with sums over #permutations.