$F$ 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2021
 arXiv:
 arXiv:2103.04769
 Bibcode:
 2021arXiv210304769C
 Keywords:

 Mathematics  Combinatorics;
 05E45;
 52B05
 EPrint:
 20 pages, 10 figures. Comments are very welcome