The Hopf algebra of integer binary relations
Combinatorics
2020-02-07 v1
Abstract
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 Malvenuto-Reutenauer algebra on permutations, the Loday-Ronco algebra on planar binary trees, and the Chapoton algebras on ordered partitions and on Schr\"oder trees. We also derive from our construction new Hopf structures on intervals of the weak order on permutations and of the Tamari order on binary trees.
Cite
@article{arxiv.1807.03277,
title = {The Hopf algebra of integer binary relations},
author = {Vincent Pilaud and Viviane Pons},
journal= {arXiv preprint arXiv:1807.03277},
year = {2020}
}
Comments
30 pages, 14 figures