Abstract
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.
Recommended Citation
Langholz, Nathan and Usset, Joe
(2008)
"Counting Containment Partitions,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 9:
Iss.
2, Article 5.
Available at:
https://scholar.rose-hulman.edu/rhumj/vol9/iss2/5
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