ABSTRACT
So far we have seen how to define and count discrete objects using combinatorial calculus. Next we try to understand characteristics of a typical element of the class. We can use multivariable generating functions to compute statistical information about combinatorial properties of the objects. The number of occurrences of a pattern, or the number of atoms of particular type – these are examples of parameters: integer valued functions evaluated on elements in a combinatorial class. We extend the coefficient ring of power series to incorporate more variables to track this additional information. It is important to understand the algebraic context of a multivariate series, particularly when we consider it as analytic objects. For now, we manipulate the series formally using addition, multiplication and quasi inverse, as in the univariate case.
