Laboratoire d'informatique de l'IGM, Université de Marne-la-Vallée / Paris-Est
5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée
cedex 2, France
E-mail : prenom.nom @ gmail.com
A self-dual Hopf algebra on set partitions, submitted (pdf)
The main contribution of this article is to provide a combinatorial Hopf
algebra on set partitions, which can be seen as a Hopf subalgebra of the
free quasi-symmetric functions, and which is free, cofree and self-dual.
This algebraic construction comes naturally from a combinatorial algorithm,
an analogous of the Robinson-Schensted correspondence on set partitions.
We also introduce a new partial order on set partitions. We explain how
these objects are related to each others through our Hopf algebra.
On some Hopf algebras of type B , prepublication (pdf)
It is well known that permutations, binary trees and compositions are strongly related together
through mathematical objects such that Hopf algebras (free quasi-symmetric functions or
Malvenuto-Reutenaeur algebra, Loday-Ronco algebra, noncommutative symmetric functions)
equipped with their posets (weak order, Tamari lattice, boolean lattice inclusion).
This article is an attempt to reproduce this theory for type B. It then appears that new
objects of poset theory appears : this paper introduces the multi-interval notion.
A new construction of the Loday-Ronco Algebra, FPSAC 2006 poster section (pdf)
Algebraic constructions on set partitions, FPSAC 2007 oral presentation (pdf)
"Des mots aux objets combinatoires", Journées jeunes
chercheurs UMLV 2006 (pdf)
"A new reading of Viennot's shadow lines", 56-th Séminaire Lotharingien de Combinatoire (pdf)