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