Multipartitions and Modular Forms
Authors:Allison Arnold-Roksandich, Zoe Jansen, Anthony Lazzaro
Mentor:Holly Swisher, Associate Professor of Mathematics, Oregon State University
Partition theory, an area of combinatorics and number theory, is deeply linked to the theory of modular forms. In 2008, Ahlgren and Treneer, recognized rank difference functions for partitions as modular or mock modular objects. Here, we work to classify $k$-component multipartitions in a similar manner. Ultimately, we relate restricted $k$-rank generating functions and $k$-rank difference functions to weakly holomorphic modular forms.