UAH > Math > Math Club > Luncheon Talk 2/7/2002
A partition of a number is a representation of this number as the sum of positive integers. For example, the five partitions of 4 are 4, 3 + 1, 2 + 2, 2 + 1 + 1 and 1 + 1 + 1 + 1. This simple notion appears to belong solely to the domain of number theory. However, through the utilization of generating functions, partition theory can be used to prove complex identities from analysis. An example of this is Fabian Franklin's remarkable proof of Euler's pentagonal number theorem:
This talk will consist of short introduction to partition theory and generating functions and a presentation of Franklin's partition theoretic proof of the pentagonal number theorem.