Murray State Theses and Dissertations
Abstract
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
2018
Year degree awarded
2018
Author's Keywords
distributive lattice, diamond colored, poset, Cartan, NNG
Thesis Advisor
Dr. Robert Donnelly
Committee Member
Dr. Elizabeth Donovan
Committee Member
Dr. Timothy Schroeder
Document Type
Thesis
Recommended Citation
Atkins, William, "Distributive lattice models of the type C one-rowed Weyl group symmetric functions" (2018). Murray State Theses and Dissertations. 101.
https://digitalcommons.murraystate.edu/etd/101
Included in
Algebra Commons, Discrete Mathematics and Combinatorics Commons, Number Theory Commons, Other Mathematics Commons, Set Theory Commons