Number Theory Talks

Spring 2011

Calendar

March 23

Number Theory Seminar

2:30 - 3:20 pm.,

PSA 108

Matthias Beck,

San Francisco State University

Integer partitions from a geometric viewpoint

Abstract. The study of partitions and compositions (i.e., ordered partitions) of integers goes back centuries and has applications in various areas within and outside of number theory. Partition analysis is full of beautiful — and sometimes surprising — identities, starting with Euler’s classic theorem that the number of partitions of an integer k into odd parts equals the number of partitions into distinct parts. Motivated by work of G. Andrews et al from the last 1½ decades, we will show how one can shed light to certain classes of partition identities by interpreting partitions as integer points in polyhedra. Our approach yields both short proofs of known results and new theorems. This is joint work with Ben Braun, Ira Gessel, Nguyen Le, Sunyoung Lee, and Carla Savage.