Strong coincidence and overlap coincidence
Copyright policy )Strong coincidence and overlap coincidence
We show that strong coincidences of a certain many choices of control points are equivalent to overlap coincidence for the suspension tiling of Pisot substitution. The result is valid for degree $\ge 2$ as well, under certain topological conditions. This result gives a converse of the paper by Akiyama-Lee and elucidates the tight relationship between two coincidences.
By mistake, I did not put this on ArXiv earlier
Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc., Pisot number, Multi-dimensional shifts of finite type, tiling dynamics, Dynamical Systems (math.DS), self-affine tiling, substitution, coincidence, FOS: Mathematics, Quasicrystals and aperiodic tilings in discrete geometry, Mathematics - Dynamical Systems, pure discrete spectrum
Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc., Pisot number, Multi-dimensional shifts of finite type, tiling dynamics, Dynamical Systems (math.DS), self-affine tiling, substitution, coincidence, FOS: Mathematics, Quasicrystals and aperiodic tilings in discrete geometry, Mathematics - Dynamical Systems, pure discrete spectrum
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