S.Duzhin COMBINATORICS Lecture 4: Combinatorial species According to N. Bourbaki, a structure in a set U is an element of a tower of sets over U . ... De nition. ... 1) Two species, F 1 and F 2 , are said to be equipotent, if the sets F 1 [U ] and F 2 [U ] have equal cardinality for any nite set U . ... The type generating series of a combinatorial species F is ~ F (x) = 1 X n=0 ~ f n x n ; where ~ f n = jF [n]=  j is the number of F -structures in a set of n elements considered up to isomorphism. ...