Integer Partitions and their Applicationto Quantum Physics

Abstract

Combinatorial mathematics is not frequently associated with quantum physics. However, work in one discipline can motivate investigations in the other. A recent conjecture regarding allowed multiplets in the composite fermion model led to a proof of the unimodality of restricted partitions with duplicate or consecutive parts. This in turn, allowed the original physics conjecture to be verified. The goal of my research is to use the KOH theorem to explore and identify other special sets of restricted integer partitions and use those sets to further generalize the conjecture mentioned above.