I'm doing a small research project into these but their Wiki page and other pages I've looked at just detail what they are, and their properties.
Does anyone know of any real world applications or some interesting facts besides their properties?
2026-03-27 23:32:03.1774654323
Real world uses or interesting facts about/for Associahedron or Permutohedron
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For some interesting connections of the combinatoric relations underlying the structure of these polytopes to other areas of mathematics, see
1) Why is there a connection between enumerative geometry and nonlinear waves?
2) Relating face polytopes of permutohedra to integer partitions
3) Why do polytopes pop up in Lagrange inversion?
4) Guises of the Stasheff polytopes, associahedra ...
5) Important formulas in combinatorics
6) What is Lagrange inversion good for?
For me, the most interesting connections follow from the relations to multiplicative and compositional inversion.