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This article is cited in 1 scientific paper (total in 1 paper)
Multi-dimensional Kronecker sequences with a small number of gap lengths
Ch. Weiss Hochschule Ruhr West
Abstract:
Recently, generalizations of the classical Three Gap Theorem to higher dimensions attracted a lot of attention. In particular, upper bounds for the number of nearest neighbor distances have been established for the Euclidean and the maximum metric. It was proved that a generic multi-dimensional Kronecker attains the maximal possible number of different gap lengths for every sub-exponential subsequence. We mirror this result in dimension $d \in \left\{ 2, 3 \right\}$ by constructing Kronecker sequences which have a surprisingly low number of different nearest neighbor distances for infinitely $N \in \mathbb{N}$. Our proof relies on simple arguments from the theory of continued fractions.} \communicated{
Keywords:
Kronecker Sequences, Nearest Neighbor Distance, Continued Fractions.
Received: 27.06.2021
Citation:
Ch. Weiss, “Multi-dimensional Kronecker sequences with a small number of gap lengths”, Diskr. Mat., 33:4 (2021), 11–18; Discrete Math. Appl., 32:1 (2022), 69–74
Linking options:
https://www.mathnet.ru/eng/dm1683https://doi.org/10.4213/dm1683 https://www.mathnet.ru/eng/dm/v33/i4/p11
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Abstract page: | 188 | Full-text PDF : | 64 | References: | 24 | First page: | 13 |
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