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

2009/12/04 by Jean-Christophe Aval, Aval, Jean-Christophe, Xavier Gérard Viennot +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.0912.0798

arxiv created 2009/12/04 · openalex publication_date 2009/12/04 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

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

Cited by

• The # product in combinatorial Hopf algebras

Related

• The # product in combinatorial Hopf algebras
• Variations of the Catalan numbers from some nonassociative binary operations
• A simple bijection between binary trees and colored ternary trees
• The structure of alternative tableaux
• Binary trees using the bookshelf and baseball constructions