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A Mattila-Sjölin theorem for simplices in low dimensions
Eyvindur Ari Palsson1, Francisco Romero Acosta1
1Department of Mathematics, Virginia Tech, Blacksburg, VA 24061 USA.
Abstract:
In this paper we show that if a compact set , , has Hausdorff dimension greater than when or when , then the set of congruence class of simplices with vertices in E has nonempty interior. By set of congruence class of simplices with vertices in E we mean
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