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Full-Text Articles in Other Mathematics
Distributive Lattice Models Of The Type C One-Rowed Weyl Group Symmetric Functions, William Atkins
Distributive Lattice Models Of The Type C One-Rowed Weyl Group Symmetric Functions, William Atkins
Murray State Theses and Dissertations
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 …
Distributive Lattice Models Of The Type B Elementary Weyl Group Symmetric Functions, Katheryn Beck
Distributive Lattice Models Of The Type B Elementary Weyl Group Symmetric Functions, Katheryn Beck
Murray State Theses and Dissertations
One of the great themes of algebraic combinatorics is the exploration of connections between ordered structures and group actions/representations. This thesis furthers this theme by presenting diamond-colored distributive lattice models of certain poly nomials that are invariant under the action of the type Bn Weyl group. Initially we realize these lattices as diamond-colored lattices of order ideals from certain vertex colored posets. We explore various coordinatizations of these lattices via partition-like elements, tableaux, and binary-type representations called tally diagrams. We also examine algebraic properties of these lattices. In particular, we prove that our type Bn lattices are effective models for …