Questions tagged [polyomino]

A polyomino is an edge-connected union of grid-aligned squares in the plane; in some contexts, they may be viewed as subsets of Z^2. This tag is for questions about the properties of polyominoes, including questions about how they tile different shapes, how they may be dissected, and assembly puzzles with a given set of polyominoes.

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Prove that any polyomino of size n > 1 and perimeter p can be built by adding 1 square to some other polyomino of size n-1 and perimeter p or p-2.

It is well known that any polyomino of size n > 1 can be built by adding a square to a smaller one. Can the same thing be proven if we add the criterion that said smaller polyomino has a perimeter not greater than the size n one? It's kind of…