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:
“When Western people train the mind, the focus is generally on the left hemisphere of the cortex, which is the portion of the brain that is concerned with words and numbers. We enhance the logical, bounded, linear functions of the mind. In the East, exercises of this sort are for the purpose of getting in tune with the unconscious—to get rid of boundaries, not to create them.”
—Edward T. Hall (b. 1914)