On this page you'll find links to my own original research, and
also interesting results from other researchers:
- Polyominoes Enumeration - results from D. H. Redelmeier, W. F. Lunnon, Kevin Gong, Uwe
Schult, Tomas Oliveira e Silva, and Tony Guttmann, Iwan Jensen
and Ling Heng Wong (2000). Includes enumeration of 2-d polyominoes
up to size 46, and 3-d polyominoes up to size 15. Includes an
explanation of what it is that we're actually counting.
- Applying Parallel Programming to the Polyomino Problem - Kevin Gong, 1991. Using parallel programming to enumerate 2-d
and 3-d polyominoes. Includes a detailed description of the rooted
translation method of Rivest for enumerating polyominoes.
- Bounding Boxes for Translation Polyominoes - Kevin Gong, 2000. Enumeration of 2-d polyominoes (unique with
respect to translation) which fit into rectangles of various sizes.
Computed for up to size 17.
- Bounding Boxes for 3-D Rotation Polyominoes - Kevin Gong, 2000. Enumeration of 2-d polyominoes (unique with
respect to 3-d rotation) which fit into rectangles of various
sizes. Computed for up to size 17.
- Pentomino Game is a Win For First Player - Hilarie Orman, University of Arizona, 1994. Hilarie Orman proved
that the standard Pentomino game on the basic 8x8 board is a win
for the first player. [external download; PostScript file; on
some browsers you may want to explicitly save the file rather
than follow the link]
I've also created a mailing list for people interested in the
mathematics of Polyominoes. To join, go to: http://groups.yahoo.com/group/polyominoes/