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.

References in corpus (2)

• Total positivity, Grassmannians, and networks
• The structure of alternative tableaux

Cited by in corpus (1)

• The # product in combinatorial Hopf algebras