Is the whole really greater than the sum of its parts? Exploring partitions of numbers
Stephanie Treneer
Graduate Student
Department of Mathematics
Univeristy of Illinois at Urbana-Champaign
A partition of a positive integer n is a sequence of positive integers that sum to n. The partition function p(n) counts the partitions of n without regard to order. This deceptively simple function has led to a rich theory. We'll look at two elementary methods for analyzing partitions: Ferrers graphs and generating functions, and then briefly discuss how the theory of modular forms has led to some recent surprising results about p(n).