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math.DS2025
Dynamics and topology of the Hat family of tilings
Michael Baake, Franz Gähler, Lorenzo Sadun
The recently discovered Hat tiling admits a 4-dimensional family of shape deformations, including the 1-parameter family already known to yield alternate monotiles. The continuous…
math.DS2024
How big is a tiling's return module?
Abigail Perryman, Lorenzo Sadun
The rank of a tiling's return module depends on the geometry of its tiles and is not a topological invariant. However, the rank of the first \v Cech cohomology giv…