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Strong coincidence and overlap coincidence

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  • 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 dimension $\ge 2$ as well, under certain topological conditions. This result gives a converse of the paper [2] and elucidates the tight relationship between two coincidences.
    Mathematics Subject Classification: Primary: 52C23; Secondary: 37B50, 11K16.


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