4 problems

Écalle–Chapoton conjecture. Any Lie element of ${\bf PBT}$ is a linear combination of L-classes.

Let $\operatorname{PreLie}$ be the operad of pre-Lie algebras, and let $\operatorname{PreLie}^{[2]}$ denote its second Veronese power. The preceding computations show that all rela…

Let $\mathscr{F}_t$ be the global series introduced from the parameterized flow series, and let $\mathsf{F}_t=-(1-t)\mathbf{N}_t\mathbf{T}\mathbf{P}_t$ be its dendriform candidate.…

Let $\mathscr{Y}=\mathscr{E}\circ\mathscr{D}^{-1}$ be the quotient series in the group $\mathsf{G}_{\operatorname{PreLie}}$, let $\mathscr{Y}_T$ be the coefficient of a rooted tree…