Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Drew Sills**, Rutgers University, asills {at} math [dot] rutgers [dot] edu**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Stanley's Partition Function and its Relation to p(n)

Speaker: **Holly Swisher**, University of Wisconsin

Date: December 2, 2004 4:30-5:30pm

Location: Hill Center, Room 425, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

Recently Richard Stanley formulated a new partition fuction t(n). This function counts the number of partitions pi for which the number of odd parts of pi is congruent to the number of odd parts in the conjugate partition pi' modulo 4. G.E. Andrews has recently proven a nice generating functin for t(n) in terms of the generating function for p(n), the usual partition function. He also showed that the mod 5 Ramanujan congruence for p(n) also holds for t(n). In light of these results, it is natural to ask the following questions: What is the size of t(n)? Are there other congruences satisfied by both t(n) and p(n)? We will address both of these questions.