Math.Combinatorics.Species.Labelled

An interpretation of species as exponential generating functions, which count labelled structures.

Documentation

labelled :: EGF -> [Integer]

Extract the coefficients of an exponential generating function as a list of Integers. Since EGF is an instance of Species, the idea is that labelled can be applied directly to an expression of the species DSL. In particular, labelled s !! n is the number of labelled s-structures on an underlying set of size n (note that labelled s is guaranteed to be an infinite list). For example:

 > take 10 $ labelled octopi
 [0,1,3,14,90,744,7560,91440,1285200,20603520]

gives the number of labelled octopi on 0, 1, 2, 3, ... 9 labels.