Tiling the plane with one tile
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
On the tiling by translation problem
Discrete Applied Mathematics
Christoffel and Fibonacci tiles
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
A linear time and space algorithm for detecting path intersection in Zd
Theoretical Computer Science
A note on a result of daurat and nivat
DLT'05 Proceedings of the 9th international conference on Developments in Language Theory
A decomposition theorem for homogeneous sets with respect to diamond probes
Computer Vision and Image Understanding
On the shape of permutomino tiles
Discrete Applied Mathematics
Combinatorial properties of double square tiles
Theoretical Computer Science
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We consider the tilings by translation of a single polyomino or tile on the square grid Z^2. It is well-known that there are two regular tilings of the plane, namely, parallelogram and hexagonal tilings. Although there exist tiles admitting an arbitrary number of distinct hexagon tilings, it has been conjectured that no polyomino admits more than two distinct parallelogram tilings. In this paper, we prove this conjecture.