Aval, Jean-Christophe; Viennot, Xavier

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

Sémin. Lothar. Comb. 63, B63h, 8 p., electronic only (2010)


Summary: 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.