Tiling the Plane with a Set of Ten Polyominoes

Abstract

There exists a linear algorithm to decide whether a polyomino tessellates the plane by translation only. On the other hand, the problem of deciding whether a set of [Formula: see text] or more polyominoes can tile the plane by translation is undecidable. We narrow the gap between decidable and undecidable by showing that it remains undecidable for a set of [Formula: see text] polyominoes, which partially solves a conjecture posed by Ollinger.