$F$- and $H$-Triangles for $\nu$-Associahedra

Abstract

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.

arXiv comment25 pages, 15 figures. Comments are very welcome

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• Sortable elements and Cambrian lattices
• Subword complexes, cluster complexes, and generalized multi-associahedra
• The enumeration of generalized Tamari intervals
• The Steep-Bounce Zeta Map in Parabolic Cataland
• The Rank Enumeration of Certain Parabolic Non-Crossing Partitions
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Cited by in corpus (1)

• Bubble Lattices II: Combinatorics