Rooted trees and an exponential-like series

Abstract

This paper deals with a group of generalized power series associated to any augmented operad, focusing on the case of the PreLie operad. The solution of flow equations using the pre-Lie structure on vector fields on an affine space gives rise to an interesting element of this group, which deserves to be called the PreLie exponential.

8 pages, 2 figures

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