Dendriform structures arise naturally in algebraic combinatorics (where they allow, for
example, the splitting of the shuffle product into two pieces) and through Rota–Baxter …

The m-Tamari lattice of F. Bergeron is an analogue of the classical Tamari order defined on
objects counted by Fuss-Catalan numbers, such as m-Dyck paths or (m+ 1)-ary trees. On …

We describe a method for constructing characters of combinatorial Hopf algebras by means
of integrals over certain polyhedral cones. This is based on ideas from resurgence theory, in …

The operad of moulds is realized in terms of an operational calculus of formal integrals
(continuous formal power series). This leads to many simplifications and to the discovery of …

Many features of classical Lie theory generalize to the broader context of algebras over Hopf
operads. However, this idea remains largely to be developed systematically. Quasi-shuffle …

We present a bijection from planar reduced trees to planar rooted hypertrees, which extends
Knuth's rotation correspondence between planar binary trees and planar rooted trees. The …

In a first part, we formalize the construction of combinatorial Hopf algebras from plactic-like
monoids using polynomial realizations. Thank to this construction we reveal a lattice …

This thesis finds its place in the interplay between algebraic and geometric combinatorics.
We focus on studying two different families of lattices in relation to the weak order: the …

We provide operadic interpretations for two Hopf subalgebras of the algebra of parking
functions. The Catalan subalgebra is identified with the free duplicial algebra on one …

Snakes are analogues of alternating permutations defined for any Coxeter group. We study
these objects from the point of view of combinatorial Hopf algebras, such as …