# MUIC Math

Mathematics at MUIC

### Internal

seminar:bh_partition

# Generalizing the First Partition Identity & Magic Configurations

Brian Hopkins
Saint Peter's University, New Jersey, USA

16:00 Wednesday, 7 June 2017, Room 3306, MUIC

### Abstract

The seminar will consist of two slightly related topics. First, we consider some very recent work on partition identities. The first such identity, due to Euler, is that the number of partitions of any positive integer $n$ using only odd parts is equal to the number of partitions of $n$ into distinct parts. A generalization was recently proven by George Andrews using generating functions. Here, we will use bijective proofs to explain the identity and some further generalizations.

After break, we will move to lighter fare (with more pictures), a long-forgotten area of mathematics called configurations. You may know the ones used in algebra and geometry named after Fano, Pappus, and Desragues. What happens when we mix configurations with the magic of magic squares? We use two techniques to find where these ideas first intersect and show that the association continues indefinitely.