# polyomino

A polyomino^{} consists of a number of identical connected squares placed
in distinct locations in the plane so that at least one side of each
square is adjacent to (i.e. completely coincides with the side of)
another square (if the polyomino consists of at least two squares).

A polyomino with $n$ squares is called an n-omino. For small $n$, polyominoes have special names. A 1-omino is called a monomino, a 2-omino a domino, a 3-omino a tromino or triomino, etc. The famous Tetris video game derives its name from the fact that the bricks are tetrominoes or 4-ominoes.

Fixed polyominoes (which are also called lattice animals)
are considered distinct if they cannot be translated into each other,
while free polyominoes must also be distinct under rotation^{} and
reflection.

The topic of how many distinct (free or fixed) n-ominoes exist for a given $n$ has been the subject of much research. It is known that the number of free n-ominoes ${A}_{n}$ grows exponentially. More precisely, it can be proven that $$.

Polyominoes are special instances of polyforms.

Title | polyomino |

Canonical name | Polyomino |

Date of creation | 2013-03-22 15:20:18 |

Last modified on | 2013-03-22 15:20:18 |

Owner | s0 (9826) |

Last modified by | s0 (9826) |

Numerical id | 10 |

Author | s0 (9826) |

Entry type | Definition |

Classification | msc 05B50 |

Defines | n-omino |

Defines | domino |

Defines | tromino |

Defines | tetromino |

Defines | fixed polyomino |

Defines | lattice animal |