Tiling the Plane with a Fixed Number of Polyominoes

Nicolas Ollinger (1)

1 LIF - Laboratoire d'informatique Fondamentale de Marseille - UMR 6166

Deciding whether a finite set of polyominoes tiles the plane is undecidable by reduction from the Domino problem. In this paper, we prove that the problem remains undecidable if the set of instances is restricted to sets of 5 polyominoes. In the case of tiling by translations only, we prove that the problem is undecidable for sets of 11 polyominoes.

Domaines: Autre [cs.OH]

Nicolas Ollinger. Tiling the Plane with a Fixed Number of Polyominoes. 2008. ⟨hal-00335781⟩