POLYOMINO_MONOHEDRAL_MATRIX
Linear System for Polyomino Monohedral Tiling

POLYOMINO_MONOHEDRAL_MATRIX, a MATLAB library which is given matrices defining a region R and a polyomino P, and returns the linear system A*x=b that must be solved for binary solutions x, that represent possible tilings of the region R by the polyomino P.

A region R is a subset of an MRxNR grid of squares.

A polyomino P is a subset of an MPxNP grid of squares.

Both objects are represented by binary matrices, with the property that there are no initial or final zero rows or columns.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

polyomino_monohedral_matrix is available in a MATLAB version.

Related Data and Programs:

polyomino_monohedral_matrix_test

Source Code:

• polyomino_embed_list.m, for each possible embedding, lists the translation necessary to to apply to the polyomino.
• polyomino_embed_number.m, reports the number of ways a polyomino can be embedded in a region.
• polyomino_equal.m, is true if two polyominoes are equal.
• polyomino_index.m, computes an index for each nonzero polyomino entry.
• polyomino_lp_write.m, writes an LP file describing a particular problem.
• polyomino_monohedral_matrix.m, determines the matrix and right hand side for a polyomino monohedral problem.
• polyomino_monohedral_variants.m, carries out reflections and rotations of a polyomino to determine which transformations yield distinct variants.
• polyomino_print.m, prints a polyomino.
• polyomino_transform.m, carries out reflections and rotations of a polyomino.
• timestamp.m, prints the YMDHMS date as a timestamp.