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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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