We present two families of diamond-colored distributive lattices – one known and one new – that we can show are models of the type C one-rowed Weyl symmetric functions. These lattices are constructed using certain sequences of positive integers that are visualized as ﬁlling the boxes of one-rowed partition diagrams. We show how natural orderings of these one-rowed tableaux produce our distributive lattices as sublattices of a more general object, and how a natural coloring of the edges of the associated order diagrams yields a certain diamond-coloring property. We show that each edge-colored lattice possesses a certain structure that is associated with the type C Weyl groups. Moreover, we produce a bijection that shows how any two aﬃliated lattices, one from each family, are models for the same type C one-rowed Weyl symmetric function. While our type C one-rowed lattices have multiple algebraic contexts, this thesis largely focusses on their combinatorial aspects.
Year manuscript completed
Year degree awarded
distributive lattice, diamond colored, poset, Cartan, NNG
Dr. Robert Donnelly
Dr. Elizabeth Donovan
Dr. Timothy Schroeder
Atkins, William, "Distributive lattice models of the type C one-rowed Weyl group symmetric functions" (2018). Murray State Theses and Dissertations. 101.