Colorado State University  Mathematical

Partitions into distinct parts and Dyson's rank

By  Maria Monks
From  Department of Mathematics
Massachusets Institute of Technology
Winner, 2009 Alice T. Schafer Prize (AWM)
When  March 23, 2009
4:00 pm
Where  Engineering E103

A partition of a positive integer n is a nonincreasing sequence of positive integers whose sum is n. Let Q(n) denote the number of partitions of n all of whose elements, or parts, are distinct. We show that a combinatorial partition invariant known as Dyson's rank provides a combinatorial interpretation of the fact that Q(n) is almost always divisible by 4. By investigating certain generating functions related to Dyson's rank for partitions into distinct parts, this gives rise to several new results in analytic number theory.

Alexander Hulpke

There will be Refreshments in Weber 117 at 3.30pm
The Colloquium counts as Seminar Credit for Mathematics Students.