2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74232In this note we introduce the concept of a shuffle product $\sq$ for planar tree polynomials and give a formula to compute the planar shuffle product $S \ \sq T$ of two finite planar reduced rooted trees $S, T.$ It is shown that $\sq$ is dual to the co-addition $Δ$ which leads to a formula for the coefficients of $Δ(f).$ It is also proved that $Δ(EXP) = EXP {\hat \otimes} EXP$ where $EXP$ is the generic planar tree exponential series, see [G]. Systems of quadratic relations for the coefficients of EXP are derived.12 pagesRings and Algebras17A50text