is a perl script for producing an antisymmetric matrix whose determinant is the square of the number of (weighted) tilings of a specified planar graph.

Input Formats

Weighted Input

Variable Weights

Using the Output

Derivation of the Kasteley Matrix
This is based largely on David Wilson's article (postscript) on the generation of random structures, which derives the Kasteleyn matrix and the algorithm on pages 2-3.

The Algorithm

An Example of the Algorithm

The program is executed by the Perl interpreter. It requires version 5 of perl, which is not the default version on Athena. For the script to be executed directly, the first line should begin #!

On Athena:

On Pfaff: