Problem Of the Week

Spring 2007

POW 11: Breaking Up is Hard to Do!

A partition of a positive integer, m, is a list of positive integers that add up to m. For example, {1,2,2,3} is a partition of 8, in fact, it is a partition of 8 with 4 parts. Since order doesn’t matter, we write the numbers in increasing order.

Let P(m,n) denote the number of partitions of m with n parts.

1. What is P(m,1)?
2. What is P(m,m)?
3. What is P(m,2)?

Due Friday, April 20^th , at Noon.

Solutions should be submitted to Dr. Maegan Bos’ mailbox in the Math office or sent via e-mail to mbos@stlawu.edu

Presentation counts! The prize-winning entry will be selected from all correct submissions, based on the clarity, creativity and elegance of the solution.

Look for the SLU POW on the Web at http://it.stlawu.edu/~math/activities/