## Figures from this paper

## 22 Citations

Exceptional and modern intervals of the Tamari lattice

- Mathematics
- 2018

In this article we use the theory of interval-posets recently introduced by Ch{\^a}tel and Pons in order to describe some interesting families of intervals in the Tamari lattices. These families are…

Meeting Covered Elements in $\nu$-Tamari Lattices

- Mathematics
- 2021

For each meet-semilattice M , we define an operator PopM : M →M by PopM (x) = ∧ ({y ∈M : y l x} ∪ {x}). When M is the right weak order on a symmetric group, PopM is the pop-stack-sorting map. We…

Two bijections on Tamari Intervals

- Mathematics
- 2013

We use a recently introduced combinatorial object, the $\textit{interval-poset}$, to describe two bijections on intervals of the Tamari lattice. Both bijections give a combinatorial proof of some…

m-dendriform algebras

- Mathematics
- 2014

The Fuss-Catalan numbers are a generalization of the Catalan numbers. They enumerate a large class of objects and in particular m-Dyck paths and m+1-ary trees. Recently, F. Bergeron defined an…

Geometry of $\nu $-Tamari lattices in types $A$ and $B$

- MathematicsTransactions of the American Mathematical Society
- 2018

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 our…

Cubic realizations of Tamari interval lattices

- Mathematics
- 2019

We introduce cubic coordinates, which are integer words encoding intervals in the Tamari lattices. Cubic coordinates are in bijection with interval-posets, themselves known to be in bijection with…

GEOMETRIC REALIZATIONS OF TAMARI INTERVAL LATTICES VIA CUBIC COORDINATES

- Mathematics
- 2020

We introduce cubic coordinates, which are integer words encoding intervals in the Tamari lattices. Cubic coordinates are in bijection with interval-posets, themselves known to be in bijection with…

An extension of Tamari lattices

- Mathematics
- 2014

For any finite path $v$ on the square grid consisting of north and east unit steps, starting at (0,0), we construct a poset Tam$(v)$ that consists of all the paths weakly above $v$ with the same…

Bijective link between Chapoton's new intervals and bipartite planar maps

- MathematicsEur. J. Comb.
- 2021

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Several generating series for flows on rooted trees are introduced, as elements in the group of series associated with the Pre-Lie operad. By combinatorial arguments, one proves identities that…