Permutrees

Viviane Pons (1) , Vincent Pilaud (2)

1 GALaC - LRI - Graphes, Algorithmes et Combinatoire (LRI)
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

We introduce permutrees, a unified model for permutations, binary trees, Cambrian trees and binary sequences. In this extended abstract, we summarize our main results describing combinatorial and geometric properties of permutrees, in particular the permutree lattices (specializing to the weak order, the Tamari, the Cambrian and the boolean lattice) and permutreehedra (specializing to the permutahedron, the associahedra, and the cube).

Keywords: Binary trees; Cambrian trees; Symmetric group; Hopf Algebra; Tamari lattice; Permutahedron; Associahedron

Domains: Combinatorics [math.CO]; Discrete Mathematics [cs.DM]

Viviane Pons, Vincent Pilaud. Permutrees. The European Conference on Combinatorics, Graph Theory and Applications (EUROCOMB'17), Aug 2017, Vienne, Austria. pp.987 - 993, ⟨10.1016/j.endm.2017.07.063⟩. ⟨hal-01575092⟩