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Block Partitions in Higher Dimensions.

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Title: Block Partitions in Higher Dimensions.
Authors: Csóka, Endre1 (AUTHOR) csokaendre@gmail.com
Source: Discrete & Computational Geometry. Jun2026, Vol. 75 Issue 4, p1288-1293. 6p.
Subjects: Discrete geometry
Abstract: Consider a set X ⊆ R d which is 1-dense, namely, it intersects every open unit ball. We show that for any n ∈ N , we can get from any point to any other point in R d in n steps so that the intermediate points are in X, and the discrepancy of the step vectors is at most 2 2 . [ABSTRACT FROM AUTHOR]
Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Consider a set X ⊆ R d which is 1-dense, namely, it intersects every open unit ball. We show that for any n ∈ N , we can get from any point to any other point in R d in n steps so that the intermediate points are in X, and the discrepancy of the step vectors is at most 2 2 . [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00454-025-00732-7
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      – TitleFull: Block Partitions in Higher Dimensions.
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              Text: Jun2026
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