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On the Number of Rich Lines in High Dimensional Real Vector Spaces

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Abstract

In this short note we use the Polynomial Ham Sandwich Theorem to strengthen a recent result of Dvir and Gopi about the number of rich lines in high dimensional Euclidean spaces. Our result shows that if there are sufficiently many rich lines incident to a set of points then a large fraction of them must be contained in a hyperplane.

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Authors and Affiliations

  1. Department of Mathematics, David Rittenhouse Labs, University of Pennsylvania, 209 s. 33rd st, Philadelphia, PA, 19104-6395, USA

    Márton Hablicsek & Zachary Scherr

Authors
  1. Márton Hablicsek
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  2. Zachary Scherr
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Correspondence to Zachary Scherr.

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Editor in Charge: János Pach

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Hablicsek, M., Scherr, Z. On the Number of Rich Lines in High Dimensional Real Vector Spaces. Discrete Comput Geom 55, 955–962 (2016). https://doi.org/10.1007/s00454-016-9774-6

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  • DOI: https://doi.org/10.1007/s00454-016-9774-6

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