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math.CO2024
Translational Aperiodic Sets of 7 Polyominoes
Chao Yang, Zhujun Zhang
Recently, two extraordinary results on aperiodic monotiles have been obtained in two different settings. One is a family of aperiodic monotiles in the plane discovered by Smith, My…
math.CO2024
Undecidability of Translational Tiling of the 4-dimensional Space with a Set of 4 Polyhypercubes
Chao Yang, Zhujun Zhang
Recently, Greenfeld and Tao disprove the conjecture that translational tilings of a single tile can always be periodic [Ann. Math. 200(2024), 301-363]. In another paper [to appear…
math.CO2024★ 1 cited
Undecidability of Translational Tiling of the 3-dimensional Space with a Set of 6 Polycubes
Chao Yang, Zhujun Zhang
This paper focuses on the undecidability of translational tiling of -dimensional space with a set of tiles. It is known that tiling with transl…