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 $$ G^\*(t) = \exp(G^\*(t)) = 1 + \dots .$$ This '$1$' at degree zero is the empty structure.

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 $F(t) $ the formula is $F(t) = \exp(G(t)) = 1 + ... $. This $1$ at degree zero is the empty structure.

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.

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 $$ G^\*(t) = \exp(G^\*(t)) = 1 + \dots .$$ This '$1$' at degree zero is the empty structure.