The Andrews-Stanley Partition Function and p(n)
by
Holly Swisher
University of Wisonsin - Madison

Let pi be a partition of n and pi' its conjugate. Define O(pi) to be the number of odd parts in the partition pi. Work of R. Stanley has led to a new partition statistic, O(pi) - O(pi'). In a recent paper, G. E. Andrews examines partitions in terms of O(pi) and O(pi'), and obtains results about a new partition function t(n), which counts partitions pi for which O(pi) is congruent to O(pi') modulo 4. Andrews' paper brings up the question "What is the relationship between t(n) and p(n)?" In this talk I will examine two different aspects of this question. First I will address the growth of t(n), proving an asymptotic formula relevant to that for p(n). Then I will discuss congruence properties for t(n).

Date received: April 30, 2004