Mathematics

We generalize overpartition rank and crank generating functions to obtain k-fold variants and give a combinatorial interpretation for each. The k-fold crank generating function is interpreted by extending the first and second residual cranks to a natural infinite family. The k-fold rank generating functions generate two families of buffered Frobenius representations, which generalize the first and second Frobenius representations studied by Lovejoy.

Thomas's major professor is Prof. Holly Swisher.