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arXiv · 2508.10067

Undecidability of Tiling the Plane with a Set of 5 Polyominoes

Yoonhu Kim
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Abstract

In this paper, we give a proof that it is undecidable whether a set of five polyominoes can tile the plane by translation. The proof involves a new method of labeling the edges of polyominoes, making it possible to assign whether two edges can match for any set of two edges chosen. This is achieved by dedicating 1 polyomino to the labeling process.

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Yoonhu Kim. 2025-08-13. Undecidability of Tiling the Plane with a Set of 5 Polyominoes. https://arxiv.org/abs/2508.10067

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