60 citations · 768 across the 56 of their papers we have counts for
6 papers · 2 filters
Cambrian triangulations and their tropical realizations
Vincent Pilaud
This paper develops a Cambrian extension of the work of C. Ceballos, A. Padrol and C. Sarmiento on -Tamari lattices and their tropical realizations. For any signature $\varepsil…
Non-kissing and non-crossing complexes for locally gentle algebras
Yann Palu, Vincent Pilaud, Pierre-Guy Plamondon
Starting from a locally gentle bound quiver, we define on the one hand a simplicial complex, called the non-kissing complex. On the other hand, we construct a punctured, marked, or…
The Hopf algebra of integer binary relations
Vincent Pilaud, Viviane Pons
We construct a Hopf algebra on integer binary relations that contains under the same roof several well-known Hopf algebras related to the permutahedra and the associahedra: the Mal…
Hopf dreams and diagonal harmonics
Nantel Bergeron, Cesar Ceballos, Vincent Pilaud
This paper introduces a Hopf algebra structure on a family of reduced pipe dreams. We show that this Hopf algebra is free and cofree, and construct a surjection onto a commutative…
The weak order on Weyl posets
Joël Gay, Vincent Pilaud
We define a natural lattice structure on all subsets of a finite root system that extends the weak order on the elements of the corresponding Coxeter group. For crystallographic ro…
Hopf algebras on decorated noncrossing arc diagrams
Vincent Pilaud
Noncrossing arc diagrams are combinatorial models for the equivalence classes of the lattice congruences of the weak order on permutations. In this paper, we provide a general meth…