Abstract
Bennett, Iosevich and Taylor proved that compact subsets of \({\mathbb R}^d\), \(d \ge 2\), of Hausdorff dimensions greater than \(\frac{d+1}{2}\) contain chains of arbitrary length with gaps in a non-trivial interval. In this paper we generalize this result to arbitrary tree configurations.
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Iosevich, A., Taylor, K. (2019). Finite Trees Inside Thin Subsets of \({\mathbb R}^{d}\). In: Karapetyants, A., Kravchenko, V., Liflyand, E. (eds) Modern Methods in Operator Theory and Harmonic Analysis. OTHA 2018. Springer Proceedings in Mathematics & Statistics, vol 291. Springer, Cham. https://doi.org/10.1007/978-3-030-26748-3_3
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DOI: https://doi.org/10.1007/978-3-030-26748-3_3
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