Greg Kuperberg
Symmetry classes of alternating-sign matrices
After the discovery of alternating-sign matrices, David Robbins (and in one case, William Mills) went on to investigate symmetry classes of alternating-sign matrices. I will describe my efforts to enumerate these symmetry classes by generalizing the Izergin-Korepin determinant and its evaluation. So far the method only enumerates some of the symmetry classes listed by Robbins, but it also leads to new classes of matrices that can also be enumerated.