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F- and H-triangles for ν-associahedra

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https://doi.org/10.5070/C62257846Creative Commons 'BY' version 4.0 license
Abstract

For any northeast path ν, we define two bivariate polynomials associated with the ν-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.

Mathematics Subject Classifications: 05E45, 52B05

Keywords: ν-Tamari lattice, ν-associahedron, F-triangle, H-triangle

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