$F$- and $H$-Triangles for $ν$-Associahedra

8 Mar 2021  ·  Cesar Ceballos, Henri Mühle ·

For any northeast path $\nu$, we define two bivariate polynomials associated with the $\nu$-associahedron: the $F$- and the $H$-triangle. We prove combinatorially that we can obtain one from the other by an invertible transformation of variables... These polynomials generalize the classical $F$- and $H$-triangles of F.~Chapoton in type $A$. Our proof is completely new and has the advantage of providing a combinatorial explanation of the relation between the $F$- and $H$-triangle. read more

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Combinatorics 05E45, 52B05