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单词 Polyomino
释义

polyomino


A polyominoMathworldPlanetmath consists of a number of identical connected squares placedin distinct locations in the plane so that at least one side of eachsquare 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 thatthe bricks are tetrominoes or 4-ominoes.

Figure 1: All distinct 1-, 2-, 3-, 4-, and 5-ominoes. Pentominoeshave been scaled in the figure to fit on the page.

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 rotationMathworldPlanetmath andreflection.

Figure 2: All distinct, fixed dominoes and trominoes.

The topic of how many distinct (free or fixed) n-ominoes exist for a givenn has been the subject of much research. It is known that thenumber of free n-ominoes An grows exponentially. More precisely, itcan be proven that 3.72n<An<4.65n.

Polyominoes are special instances of polyforms.

Titlepolyomino
Canonical namePolyomino
Date of creation2013-03-22 15:20:18
Last modified on2013-03-22 15:20:18
Owners0 (9826)
Last modified bys0 (9826)
Numerical id10
Authors0 (9826)
Entry typeDefinition
Classificationmsc 05B50
Definesn-omino
Definesdomino
Definestromino
Definestetromino
Definesfixed polyomino
Defineslattice animal
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更新时间:2025/5/4 19:19:39