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Polynomial realizations of some trialgebras

J. -C. Novelli·J. -Y. Thibon
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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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J. -C. Novelli, J. -Y. Thibon. 2006-05-02. Polynomial realizations of some trialgebras. https://arxiv.org/abs/math/0605061

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