Combinatorial Theory

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.

Mathematics Subject Classifications: 05E45, 52B05

Keywords: \(\nu\)-Tamari lattice, \(\nu\)-associahedron, \(F\)-triangle, \(H\)-triangle