Corpus ID: 237357329

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

@inproceedings{Ceballos2021FA,
title={\$F\$- and \$H\$-Triangles for \$\nu\$-Associahedra},
author={Cesar Ceballos and Henri Muhle},
year={2021}
}
• Published 2021
• Mathematics
For any northeast path ν, we define two bivariate polynomials associated with the ν-associahedron: the Fand 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 Fand 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 Fand H-triangle.

#### References

SHOWING 1-10 OF 21 REFERENCES
The Rank Enumeration of Certain Parabolic Non-Crossing Partitions
• Mathematics
• 2019
We consider $m$-divisible non-crossing partitions of $\{1,2,\ldots,mn\}$ with the property that for some $t\leq n$ no block contains more than one of the first $t$ integers. We give a closed formulaExpand
The Steep-Bounce zeta map in Parabolic Cataland
• Physics, Mathematics
• J. Comb. Theory, Ser. A
• 2020
The Steep-Bounce Conjecture is proved using a generalization of the famous zeta map in $q,t$-Catalan combinatorics, which arises in the theory of diagonal harmonics. Expand
Geometry of $\nu$-Tamari lattices in types $A$ and $B$
• Mathematics
• 2016
In this paper, we exploit the combinatorics and geometry of triangulations of products of simplices to derive new results in the context of Catalan combinatorics of $\nu$-Tamari lattices. In ourExpand
Chapoton triangles for nonkissing complexes
• Mathematics
• 2020
We continue the study of the nonkissing complex that was introduced by Petersen, Pylyavskyy, and Speyer and was studied lattice-theoretically by the second author. We introduce a theory ofExpand
On the H-triangle of generalised nonnesting partitions
• M. Thiel
• Computer Science, Mathematics
• Eur. J. Comb.
• 2014
This conjecture is proved, obtaining some structural and enumerative results on NN^(^k^)(@F) along the way, including an earlier conjecture by Fomin and Reading giving a refined enumeration by Fusz-Narayana numbers. Expand
Y-systems and generalized associahedra
• Mathematics, Physics
• 2003
The goals of this paper are two-fold. First, we prove, for an arbitrary finite root system D, the periodicity conjecture of Al. B. Zamolodchikov [24] that concerns Y-systems, a particular class ofExpand
Cluster algebras II: Finite type classification
• Mathematics
• 2002
This paper continues the study of cluster algebras initiated in math.RT/0104151. Its main result is the complete classification of the cluster algebras of finite type, i.e., those with finitely manyExpand
Many non-equivalent realizations of the associahedron
• Mathematics, Computer Science
• Comb.
• 2015
It is shown that two Hohlweg-Lange associahedra have linearly equivalent normal fans if and only if they are isometric, as a consequence of the classification of these constructions modulo linear equivalence of their normal fans. Expand
Sortable elements and Cambrian lattices
Abstract.We show that the Coxeter-sortable elements in a finite Coxeter group W are the minimal congruence-class representatives of a lattice congruence of the weak order on W. We identify thisExpand
Noncrossing Arc Diagrams, Tamari Lattices, and Parabolic Quotients of the Symmetric Group
Ordering permutations by containment of inversion sets yields a fascinating partial order on the symmetric group: the weak order. This partial order is, among other things, a semidistributiveExpand