133 citations · 795 across the 60 of their papers we have counts for
31 papers · 1 filter
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 give…
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…
Topological Mixing of Random Substitutions
Eden Miro, Dan Rust, Lorenzo Sadun +1
We investigate topological mixing of compatible random substitutions. For primitive random substitutions on two letters whose second eigenvalue is greater than one in modulus, we i…
Number of bounded distance equivalence classes in hulls of repetitive Delone sets
Dirk Frettlöh, Alexey Garber, Lorenzo Sadun
Two Delone sets are bounded distance equivalent to each other if there is a bijection between them such that the distance of corresponding points is uniformly bounded. Bounded dist…
Rotation numbers and rotation classes on one-dimensional tiling spaces
José Aliste-Prieto, Betseygail Rand, Lorenzo Sadun
We extend rotation theory of circle maps to tiling spaces. Specifically, we consider a 1-dimensional tiling space with finite local complexity and study self-maps that are…
Pattern Equivariant Mass Transport in Aperiodic Tilings and Cohomology
Michael Kelly, Lorenzo Sadun
Suppose that we have a repetitive and aperiodic tiling of , and two mass distributions and on , each pattern equivariant with respec…