Four symmetry classes of plane partitions under one roof

Details Four symmetry classes of plane partitions under one roof Four symmetry classes of plane partitions under one roof

1995-06-08

arxiv.org/abs/math/9506225v1

J. Combin. Theory Ser. A 75 (1996), no. 2, 295--315

Mathematics

Combinatorics

Scientific paper

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.

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