Based on the Connes-Kreimer Hopf algebra of rooted trees, rooted tree maps are defined as linear maps on the noncommutative polynomial algebra Q . It is known that they induce a large class of linear relations for multiple zeta values. In this paper, we show for any rooted tree f there exists a unique polynomial in Q that gives the image of the rooted tree map (f) over tilde explicitly. We also characterize the antipode maps as the conjugation by the special map tau.
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