Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA)

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pp: 299–344

DOI: 10.4171/204-1/8

The Hopf algebra of integer binary relations

Vincent Pilaud[1] and Viviane Pons[2]

(1) École Polytechnique, Palaiseau, France
(2) Université Paris-Sud, Orsay, France

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 Schröder 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.

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