Four symmetry classes of plane partitions under one roof
Combinatorics
2016-09-06 v1
Abstract
In previous paper, the author applied the permanent-determinant method of Kasteleyn and its non-bipartite generalization, the Hafnian-Pfaffian method, to obtain a determinant or a Pfaffian that enumerates each of the ten symmetry classes of plane partitions. After a cosmetic generalization of the Kasteleyn method, we identify the matrices in the four determinantal cases (plain plane partitions, cyclically symmetric plane partitions, transpose-complement plane partitions, and the intersection of the last two types) in the representation theory of sl(2,C). The result is a unified proof of the four enumerations.
Keywords
Cite
@article{arxiv.math/9506225,
title = {Four symmetry classes of plane partitions under one roof},
author = {Greg Kuperberg},
journal= {arXiv preprint arXiv:math/9506225},
year = {2016}
}