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The research demonstrates a uniquely ergodic zero entropy tiling of amenable groups, indicating significant enhancements in invariance properties.
For a countable amenable group G, we prove the existence of a uniquely ergodic zero entropy tiling of G, whose tiles have arbitrarily good invariance properties. This improves the tiling construction of Downarowicz, Huczek and Zhang (2019) by adding unique ergodicity.
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Kopacz et al. (2025) studied this question.
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