  In prior work, the authors, along with M. McClard, R. A. Proctor, and N. J.
Wildberger, studied certain distributive lattice models for the `Weyl
bialternants' (aka `Weyl characters') associated with the rank two root
systems/Weyl groups. These distributive lattices were uniformly described as
lattices of order ideals taken from certain grid-like posets, although the
arguments connecting the lattices to Weyl bialternants were case-by-case
depending on the type of the rank two root system. Using this connection with
Weyl bialternants, these lattices were shown to be rank symmetric and rank
unimodal, and their rank generating functions were shown to have beautiful
quotient-of-products expressions. Here, these results are re-derived from
scratch using completely uniform and elementary combinatorial reasoning in
conjunction with some combinatorial methodology developed elsewhere by the
second listed author.
