Rooted trees, non-rooted trees and hamiltonian B-series
  We explore the relationship between (non-planar) rooted trees and free trees, i.e. without root. We give in particular, for non-rooted trees, a substitute for the Lie bracket given by the antisymmetrization of the pre-Lie product. 
Geir Bogfjellmo, Charles H. Curry, Dominique Manchon
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