The Refined Lives of the F- and H-Vectors of Associahedra

The compositional inversions noted in the Oct. 9-th entry “Flipping Functions with Permutohedra” have counterparts with respect to the associahedra, or Stasheff polytopes. The h-polynomials of the simplicial complexes dual to the associahedra (see the Narayana number triangle OEIS-A001263) can be refined as OEIS-A134264 for the coefficients of an indirect Lagrange method for determining the compositional inverse of a function, whereas the corresponding f-polynomials (see OEIS-A033282) can be refined as the unsigned polynomials in OEIS-A133437 for the coefficients of a Lagrange inversion for an ordinary generating function.

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