Polynomial realizations of some trialgebras
J.-C. Novelli, J.-Y. Thibon
TL;DR
This paper constructs polynomial realizations of various combinatorial Hopf algebras related to set compositions, plane trees, and segmented compositions, detailing their algebraic structures and bases.
Contribution
It introduces polynomial realizations of trialgebra structures for multiple combinatorial Hopf algebras, providing explicit bases and internal products.
Findings
Polynomial realizations of Hopf algebras are achieved.
Trialgebra structures are explicitly described.
Multiple bases and internal products are constructed.
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.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Advanced Topics in Algebra