Kostant’s Partition Function and Multiplex Juggling Sequences by Anthony Simpson ’19, Mathematics Senior Thesis Defense, Wednesday, April 10, 1-1:45 pm, Stetson Court Classroom 101
Abstract: In this thesis, we show the combinatorial equivalence of two combinatorial problems. The first is partitioning the weights of classical Lie algebras using the positive roots of the Lie algebra. The second problem is counting multiplex juggling sequences with certain properties. We first solve a problem previously posed by Harris, Insko, and Omar, then show the general combinatorial equivalence of these problems. Our work focuses primarily on partitioning in a Lie algebra of type A, but we relate the results to partitions of weights of Lie algebras of other types and show some equivalences between two extensions of multiplex juggling sequences.