March 31, 2011: Breaking up is hard to do: Investigations in integer partitions

February 20th, 2011 by Dana Ernst

Title: Breaking up is hard to do: Investigations in integer partitions

Date: Thursday, March 31, 2011

Location: Hyde 349

Time: 4:00-5:00PM (Pizza at 3:30PM in Hyde 349)

Speaker: Andrew Schultz (Wellesley College)

Abstract: One of the early mathematical puzzles you might have been asked as a child is to think of all the ways you can add up numbers to get 4.  Of course 2+2=4 is famous, but most children familiar with addition will also be able to tell you that 4 can be expressed as 1+1+2,  1+1+1+1, or 1+3.  If we throw in the less-than-thrilling equality 4=4, this gives us a total of 5 ways to write 4 as a sum of positive numbers.  Listing the number of ways to write 100 as a sum of positive integers will take you a little longer: there are almost 200 million different possibilities.

The function p(n) is the function which keeps count of the number of ways of writing an integer n as a sum of positive integers, and mathematicians have long been interested in its properties.  In this talk we will discuss a number of very interesting results for this seemingly straightforward function, and along the way we will meet some of the greatest mathematical minds in history.

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