4 papers · 1 filter
Cellular diagonals of permutahedra
Bérénice Delcroix-Oger, Guillaume Laplante-Anfossi, Vincent Pilaud +1
We provide a systematic enumerative and combinatorial study of geometric cellular diagonals on the permutahedra. In the first part of the paper, we study the combinatorics of certa…
Hochschild polytopes
Vincent Pilaud, Daria Poliakova
The -multiplihedron is a polytope whose faces correspond to -painted -trees, and whose oriented skeleton is the Hasse diagram of the rotation lattice on binary -pai…
Celebrating Loday's Associahedron
Vincent Pilaud, Francisco Santos, Günter M. Ziegler
We survey Jean-Louis Loday's vertex description of the associahedron, and its far reaching influence in combinatorics, discrete geometry and algebra. We present in particular four…
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…