  A method of Proctor [European J. Combin. 5 (1984), no. 4, 331-350] realizes
the set of arbitrary plane partitions in a box and the set of symmetric plane
partitions as bases of linear representations of Lie groups. We extend this
method by realizing transposition and complementation of plane partitions as
natural linear transformations of the representations, thereby enumerating
symmetric plane partitions, self-complementary plane partitions, and
transpose-complement plane partitions in a new way.

Combinatorics