Séminaire Lotharingien de Combinatoire, B53d (2005), 16 pp.
Inversion of Integral Series Enumerating Planar Trees
We consider an integral series f(X,t) which
depends on the choice of a set X of labelled planar rooted
prove that its inverse with respect to composition is of the form
f(Z,t) for another set Z of trees, deduced from
X. The proof is self-contained, though inspired by the Koszul
duality theory of quadratic operads. In the same vein we give a
conceptual proof for the formulas giving the coefficients of the
inverse with respect to composition of the generic formal power
Received: November 15, 2004.
Accepted: November 11, 2005.
Final Version: November 23, 2005.
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