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The empty structure is ''disconnected'' and the definition of a tree is ''connected acyclic graph''. For example to get from the generating series $G(t)$ of a connected species to the generating series of the set of its structures $G^*(t) F(t) $ the formula is $$ G^*(t) F(t) = \exp(G^*(t)) exp(G(t)) = 1 + \dots .$$ .. $. This '$1$' $1$ at degree zero is the empty structure. |
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The empty structure is ''disconnected'' and the definition of a tree is ''connected acyclic graph''. For example to get from the generating series $G(t)$ of a connected species to the generating series of the set of its structures $ G^(t) G^*(t) $ the formula is $$ G^(t) G^*(t) = \exp(G^*(t)) = 1 + \dots ... $$. This'$1$$$ This '$1$' at degree zero is the empty structure. |
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The empty structure is ''disconnected'' and the definition of a tree is ''connected acyclic graph''. For example to get from the generating series $G(t)$ of a connected species to the generating series of the set of its structures $ G^(t) $ the formula is $$ G^(t) = \exp(G^*(t)) = 1 + ... $$. This'$1$' at degree zero is the empty structure. |
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