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arXiv · 2403.13472

A proof of Ollinger's conjecture: undecidability of tiling the plane with a set of $8$ polyominoes

Chao Yang·Zhujun Zhang
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Abstract

We give a proof of Ollinger's conjecture that the problem of tiling the plane with translated copies of a set of $8$ polyominoes is undecidable. The techniques employed in our proof include a different orientation for simulating the Wang tiles in polyomino and a new method for encoding the colors of Wang tiles.

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Chao Yang, Zhujun Zhang. 2024-03-20. A proof of Ollinger's conjecture: undecidability of tiling the plane with a set of $8$ polyominoes. https://doi.org/10.1007/s00454-024-00706-1

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