Mathematical Colloquium |
Partitions into distinct parts and Dyson's rank |
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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 |
Abstract | 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. |
Further Information |
Alexander Hulpke |
There will be Refreshments in Weber 117 at 3.30pm
The Colloquium counts as Seminar Credit for Mathematics Students.