Geodesic
The Product of Trees in the Loday-Ronco Algebra through Catalan Alternative Tableaux
Séminaire lotharingien de combinatoire, Tome 63 (2010)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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. 

@article{SLC_2010_63_a7,
     author = {Jean-Christophe Aval and Xavier Viennot},
     title = {The {Product} of {Trees} in the {Loday-Ronco} {Algebra} through {Catalan} {Alternative} {Tableaux}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {63},
     year = {2010},
     url = {http://geodesic.mathdoc.fr/item/SLC_2010_63_a7/}
}
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Jean-Christophe Aval; Xavier Viennot. The Product of Trees in the Loday-Ronco Algebra through Catalan Alternative Tableaux. Séminaire lotharingien de combinatoire, Tome 63 (2010). http://geodesic.mathdoc.fr/item/SLC_2010_63_a7/