Combinatorial addition formulas

Pierre Auger, Gilbert Labelle, Pierre Leroux LaCIM Universite du Quebec a Montreal

To appear at Formal Power Series and Algebraic Combinatorics (FPSAC01), Tempe, Arizona (USA), May 20-26, 2001


We derive addition formulas at the combinatorial level, that is equations of the form $F(X_1+X_2+\cdots+X_k)=\Phi_F (X_1,X_2,\ldots,X_k)$, where $F=F(X)$ is a given combinatorial species and $\Phi_F$ is a species on $k$ sorts of singletons $X_1,X_2,\ldots,X_k,$ depending on $F$.

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