polünoomile

Polünoomile refers to a polyomino, a plane geometric figure formed by joining unit squares edge to edge. The squares must share full sides; shapes connected only at corners do not form a polyomino. Variants arise in how rotations and reflections are treated: free polyominoes consider rotations and reflections as the same shape, one-sided polyominoes count reflections as distinct, and fixed polyominoes treat every orientation as a separate object.

Common terminology by order includes monomino (1 square), domino (2), tromino (3), tetromino (4), pentomino (5), and hexomino (6). Some families are widely studied: tetrominoes are famous from the game Tetris, while pentominoes consist of 12 free shapes named after letters F, I, L, N, P, T, U, V, W, X, Y, and Z.

The term polyomino was coined by Solomon W. Golomb in 1953, and since then the subject has become part of recreational mathematics and combinatorial tiling. Enumeration of polyominoes grows rapidly with the number of squares, and complete counts are known only for relatively small orders, typically requiring computer methods for larger n.

Applications include tiling problems (can a region be covered completely by copies of a given polyomino?), puzzle design, and theoretical studies in geometry and algorithms. Polyomino theory intersects with topics such as tiling, covering, and computational complexity, illustrating rich connections between simple geometric rules and complex combinatorial questions.