The product of trees in the Loday-Ronco algebra through Catalan alternative tableaux

Jean-Christophe Aval (1) , Xavier Gérard Viennot (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

The aim of this note is to show how the introduction of certain tableaux, called Catalan alternative tableaux, provides a very simple and elegant description of the product in the Hopf algebra of binary trees defined by Loday and Ronco. Moreover, we use this description to introduce a new associative product on the space of binary trees.

Domaines: Combinatoire [math.CO]

Jean-Christophe Aval, Xavier Gérard Viennot. The product of trees in the Loday-Ronco algebra through Catalan alternative tableaux. Seminaire Lotharingien de Combinatoire, 2010, 63, pp.B63h. ⟨hal-00438581⟩