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