A sufficient condition for aperiodicity of striped Wang tiles is established via parabola geometry, enabling explicit constructions of aperiodic sets for every pair of quadratic irrationals as vertical and horizontal stripe densities.
Pytheas Fogg.Substitutions in dynamics, arithmetics and combinatorics, volume 1794 of Lecture Notes in Mathematics
3 Pith papers cite this work. Polarity classification is still indexing.
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Pin classes exhibit a phase transition at μ ≈ 3.28277 with countably many below the threshold and uncountably many at it; all growth rates below μ are classified via periodic pin permutations.
Every generalized Bratteli diagram is isomorphic to an irreducible version, with new notions of complete irreducibility linked to topological properties of the path space and tail equivalence.
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Isomoprhism of generalized Bratteli diagrams
Every generalized Bratteli diagram is isomorphic to an irreducible version, with new notions of complete irreducibility linked to topological properties of the path space and tail equivalence.