Séminaire Lotharingien de Combinatoire, 85B.44 (2021), 12 pp.

Cesar Ceballos and Henri Mühle

F- and H-Triangles for ν-Associahedra

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 nature of the relation between the F- and H-triangle.

Received: December 1, 2020. Accepted: March 1, 2021. Final version: April 29, 2021.

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