reid_tiling


reid_tiling, a Python code which uses the reduced row echelon format (RREF) of a matrix to determine several tilings of the Reid polyomino.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

reid_tiling is available in a Python version.

Related Data and Programs:

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

pentominoes, a Python code which forms or plots any of the 12 members of the pentomino family, shapes formed from 5 adjacent squares.

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

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.

rref2, a Python code which involves a user-written approach to compute the reduced row echelon form (RREF) of a matrix, which can be used to analyze matrices which are square or rectangular, singular or invertible.

Reference:

  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 revised on 08 April 2025.