Generate Polyominoes in APL

I have won the 3rd Place on 2013 APL Problem Solving Competition by solving one problem, the mathematical one. The judges decided that:

Chao used Dfns to produce clean, compact, and efficient code.  His solution for PolyGen was more than twice as fast as the next closest entry.

The other two problems are too messy for me to handle. Ahh, I’m not the engineering type.

Here is my submission with comments, and the problem itself can be seen here.

50 lines (include comments) for $750, not so bad.