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A remark on sets with few distances in ℝ^d

Petrov, Fedor and Pohoata, Cosmin (2019) A remark on sets with few distances in ℝ^d. . (Unpublished)

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A celebrated theorem due to Bannai-Bannai-Stanton says that if A is a set of points in ℝ^d, which determines s distinct distances, then |A| ≤ (d+s/s). In this note, we give a new simple proof of this result by combining Sylvester's Law of Inertia for quadratic forms with the proof of the so-called Croot-Lev-Pach Lemma from additive combinatorics.

Item Type:Report or Paper (Discussion Paper)
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Record Number:CaltechAUTHORS:20200110-145848460
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100640
Deposited By: Tony Diaz
Deposited On:11 Jan 2020 00:30
Last Modified:11 Jan 2020 00:30

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