The study of integer partitions has wide applications to mathematics, mathematical physics, and statistical mechanics. We consider the problem of ?nding a generalized ap- proach to counting the partitions of an integer n that contain a partition of a ?xed integer k. We use generating function techniques to count containment partitions and verify exper- imental results using a self-made in program Mathematica. We have found explicit solutions to the problem for general n with k=1, 2, 3, 4, 5, 6. We also discuss open questions and ideas for future work.

Author Bio

Nathan Langholz (langholz@ucla.edu) just completed his Bachelor of Arts degree in May 2008 from St. Olaf College in Northfield, MN. He graduated with a major in Mathematics and concentration in Statistics. At St. Olaf he was a member of the varsity soccer team, and also enjoys fishing, golfing, and traveling. In the fall of 2008, he will begin working towards a Ph.D. in statistics at UCLA. He originally hails from the small town of Decorah, IA.

Upon graduation in 2004 from Henry Sibley High School (St. Paul, MN), Joe Usset (joeusset@gmail.com) enrolled at St. Olaf College in Northfield, MN. At St. Olaf he participated in varsity soccer while working toward a bachelor�s degree. In May 2008, he graduated with a mathematics major and statistics concentration. In August he is set to move to Raleigh, NC, where he will start work on a masters degree in statistics at North Carolina State University. His research interests include genetics, environmental statistics, and sports statistics.