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Séminaire Lotharingien de Combinatoire, B63h (2010), 8 pp.

# Jean-Christophe Aval and Xavier Viennot

# The Product of Trees in the Loday-Ronco Algebra through Catalan Alternative Tableaux

**Abstract.**
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.

Received: January 14, 2010.
Accepted: June 14, 2010.

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