55 citations · 113 across the 8 of their papers we have counts for
9 papers
Tridendriform structure on combinatorial Hopf algebras
Emily Burgunder, Maria Ronco
We extend the definition of tridendriform bialgebra by introducing a weight q. The subspace of primitive elements of a q-tridendriform bialgebra is equipped with an associative pro…
Combinatorial Hopf algebras
Jean-Louis Loday, Maria O. Ronco
We define a "combinatorial Hopf algebra" as a Hopf algebra which is free (or cofree) and equipped with a given isomorphism to the free algebra over the indecomposables (resp. the c…
Shuffle bialgebras
Maria Ronco
The goal of our work is to study the spaces of primitive elements of the Hopf algebras associated to the permutaedra and the associaedra. We introduce the notion of shuffle and pre…
Coassociative magmatic bialgebras and the Fine numbers
Ralf Holtkamp, Jean-Louis Loday, Maria Ronco
We prove a structure theorem for the connected coassociative magmatic bialgebras. The space of primitive elements is an algebra over an operad called the primitive operad. We prove…
On the structure of cofree Hopf algebras
Jean-Louis Loday, Maria Ronco
We prove an analogue of the Poincare'-Birkhoff-Witt theorem and of the Cartier-Milnor-Moore theorem for non-cocommutative Hopf algebras. The primitive part of a cofree Hopf algebra…
Weak Bruhat order on the set of faces of the permutahedra
Patricia Palacios, Maria Ronco
We extend the weak Bruhat order of a finite Coxeter group to the set of its coclasses, modulo parabolic standard subgroups. We use this order to describe associative algebra struct…