polyomino_parity, a Python code which uses parity considerations to determine whether a given set of polyominoes can tile a specified region.


The computer code and data files made available on this web page are distributed under the MIT license


polyomino_parity is available in a MATLAB version and an Octave versionand a Python version.

Related Data and Programs:

boundary_word, a Python code which describes the outline of an object on a grid of squares, using a string of symbols that represent the sequence of steps tracing out the boundary.

diophantine_nd, a Python code which is given a Diophantine equation in N variables, and returns all strictly positive solutions, or all nonnegative solutions.

pariomino, a Python code which considers pariominoes, which are polyominoes with a checkerboard parity.

polyominoes, a Python code which defines, solves, and plots a variety of polyomino tiling problems, which are solved by a direct algebraic approach involving the reduced row echelon form (RREF) of a specific matrix, instead of the more typical brute-force or backtracking methods.


  1. Marcus Garvie, John Burkardt,
    A new mathematical model for tiling finite regions of the plane with polyominoes,
    Contributions to Discrete Mathematics,
    Volume 15, Number 2, July 2020.
  2. Solomon Golomb,
    Polyominoes: Puzzles, Patterns, Problems, and Packings,
    Princeton University Press, 1996,
    ISBN: 9780691024448

Source Code:

Last modified on 17 June 2020.