Polynomial realizations of some trialgebras

2006/05/02 by Jean-Christophe Novelli, Novelli, J. -C., Jean‐Yves Thibon +1 · 5 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.math/0605061

openalex publication_date 2006/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We realize several combinatorial Hopf algebras based on set compositions, plane trees and segmented compositions in terms of noncommutative polynomials in infinitely many variables. For each of them, we describe a trialgebra structure, an internal product, and several bases.

Citations

• Weak Bruhat order on the set of faces of the permutahedra
• A Hopf algebra of parking functions

Cited by

• Fundamental and homogeneous bases of Hopf algebras built from nonsymmetric operads
• Hopf Algebras and Markov Chains
• Hopf algebras of diagrams
• A theory of pictures for quasi-posets
• Polynomial realizations of some combinatorial Hopf algebras

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