7 citations · 7 across the 1 of their papers we have counts for
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Kasteleyn cokernels
Greg Kuperberg
We consider Kasteleyn and Kasteleyn-Percus matrices, which arise in enumerating matchings of planar graphs, up to matrix operations on their rows and columns. If such a matrix is d…
Symmetry classes of alternating-sign matrices under one roof
Greg Kuperberg
In a previous article [math.CO/9712207], we derived the alternating-sign matrix (ASM) theorem from the Izergin-Korepin determinant for a partition function for square ice with doma…
An exploration of the permanent-determinant method
Greg Kuperberg
The permanent-determinant method and its generalization, the Hafnian-Pfaffian method, are methods to enumerate perfect matchings of plane graphs that was discovered by P. W. Kastel…
Another proof of the alternating sign matrix conjecture
Greg Kuperberg
Robbins conjectured, and Zeilberger recently proved, that there are 1!4!7!...(3n-2)!/n!/(n+1)!/.../(2n-1)! alternating sign matrices of order n. We give a new proof of this result…