Hopf Algebras of Graphs

Jean-Christophe Novelli (1) , Jean-Yves Thibon (1) , Nicolas M. Thiéry (2)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 LAPCS - Laboratoire de Probabilités, Combinatoire et Statistique

We define graded Hopf algebras with bases labeled by various types of graphs and hypergraphs, provided with natural embeddings into an algebra of polynomials in infinitely many variables. These algebras are graded by the number of edges and can be considered as generalizations of symmetric or quasi-symmetric functions.

Domaines: Combinatoire [math.CO]

Jean-Christophe Novelli, Jean-Yves Thibon, Nicolas M. Thiéry. Hopf Algebras of Graphs. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2004, 339 (9), pp.607--610. ⟨10.1016/j.crma.2004.09.012⟩. ⟨hal-00632273⟩