arXiv:2611.14812v1 Announce Type: new Abstract: We examine the relationship between the Hopf algebra on nonplanar binary forests, previously defined by the author, and a Hopf algebra defined by Bruned and used in the renormalization of stochastic PDEs. We show that Bruned's Hopf algebra and its reduced analogue, previously studied by Foissy in the context of combinatorial twisted bialgebras, are dual to Hopf algebras derived from pre-Lie insertion operations respecting the number of leaves, which induce leaf-based gradings on the dual Hopf algebras. We compute Hochschild 1-cocycles for these Hopf algebras and show that Bruned's Hopf algebra satisfies a similar universal property as the Connes-Kreimer Hopf algebra.
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