Tiling the Plane with a Fixed Number of Polyominoes

Authors:
Nicolas Ollinger
Affiliations:
Laboratoire d'informatique fondamentale de Marseille (LIF), Aix-Marseille Université, CNRS, Marseille, France 13013
Venue:
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Year:
2009

Citing 3
Cited 1

Tilings and patterns

Tilings and patterns
Aperiodic tiles

Discrete & Computational Geometry
Decision problems for semi-Thue systems with a few rules

Theoretical Computer Science - Insightful theory

From linear partitions to parallelogram polyominoes

DLT'11 Proceedings of the 15th international conference on Developments in language theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.