An Algebraic Invariant for Substitution Tiling Systems
classification
🧮 math.DS
math.COmath.MG
keywords
tilingsinvariantsubstitutionsystemsalgebraicanalysiscomputeconsider
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We consider tilings of Euclidean spaces by polygons or polyhedra, in particular, tilings made by a substitution process, such as the Penrose tilings of the plane. We define an isomorphism invariant related to a subgroup of rotations and compute it for various examples. We also extend our analysis to more general dynamical systems.
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