3 papers
math.CO2025
On the Undecidability of Tiling the -dimensional Space with a Set of Polycubes
Chao Yang, Zhujun Zhang
Translational tiling problems are among the most fundamental and representative undecidable problems in all fields of mathematics. Greenfeld and Tao obtained two remarkable results…
math.CO2025
Undecidability of Translational Tiling of the Plane with Four Tiles
Chao Yang, Zhujun Zhang
The translational tiling problem, dated back to Wang's domino problem in the 1960s, is one of the most representative undecidable problems in the field of discrete geometry and com…
math.CO2025
Undecidability of Translational Tiling of the Plane with Orthogonally Convex Polyominoes
Chao Yang, Zhujun Zhang
The first undecidability result on the tiling is the undecidability of translational tiling of the plane with Wang tiles, where there is an additional color matching requirement. L…