2025/01/05 by Pierre Clavier, Clavier, Pierre J., Douglas Modesto +1
Mathematics · #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2501.02557
openalex publication_date 2025/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct and study new generalisations to rooted trees and forests of some properties of shuffles of words. First, we build a coproduct on rooted trees which, together with their shuffle, endow them with bialgebra structure. We then caracterize the coproduct dual to the shuffle product of rooted forests and build a product on rooted trees to obtain the bialgebra dual to the shuffle bialgebra. We then characterize and enumerate primitive trees for the dual coproduct. Finally, using modified shuffles of rooted forests, we prove a property in the category of Rota-Baxter algebras.