Enumerative Combinatorics - Generating Functions

Generating Functions

Generating functions are used to describe families of combinatorial objects. Let denote the family of objects and let F(x) be its generating function. Then:

Where denotes the number of combinatorial objects of size n. The number of combinatorial objects of size n is therefore given by the coefficient of . Some common operation on families of combinatorial objects and its effect on the generating function will now be developed. The exponential generating function is also sometimes used. In this case it would have the form:

Read more about this topic:  Enumerative Combinatorics

Famous quotes containing the word functions:

    Let us stop being afraid. Of our own thoughts, our own minds. Of madness, our own or others’. Stop being afraid of the mind itself, its astonishing functions and fandangos, its complications and simplifications, the wonderful operation of its machinery—more wonderful because it is not machinery at all or predictable.
    Kate Millett (b. 1934)