OFFSET
1,2
COMMENTS
(n,k)-polyominoes are disconnected polyominoes with n visible squares and k transparent squares. Importantly, k must be the least number of transparent squares that need to be converted to visible squares to make all the visible squares connected. Note that a regular polyomino of order n is a (n,0)-polyomino, since all its visible squares are already connected. For more details see the paper by Kamenetsky and Cooke.
LINKS
Dmitry Kamenetsky and Tristrom Cooke, Tiling rectangles with holey polyominoes, arXiv:1411.2699 [cs.CG], 2015.
EXAMPLE
We can represent these polyominoes as binary matrices, where 1 means visible square and 0 means transparent square. Note that we need to flip (change to 1) two 0's to make all the 1's connected. This also means that the Manhattan distance between any pair of 1's is at most 3. Here are all such polyominoes for n=2:
1001 100
001
CROSSREFS
KEYWORD
nonn,more,changed
AUTHOR
Dmitry Kamenetsky, May 05 2017
EXTENSIONS
a(6) corrected and a(7)-a(10) from John Mason, Feb 15 2025
STATUS
approved