Geodesic
On Cartesian products which determine few distinct distances
Cosmin Pohoata1
1California Institute of Technology
The electronic journal of combinatorics, Tome 26 (2019) no. 1
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Every set of points $\mathcal{P}$ determines $\Omega(|\mathcal{P}| / \log |\mathcal{P}|)$ distances. A close version of this was initially conjectured by Erdős in 1946 and rather recently proved by Guth and Katz. We show that when near this lower bound, a point set $\mathcal{P}$ of the form $A \times A$ must satisfy $|A - A| \ll |A|^{2-\frac{2}{7}} \log^{\frac{1}{7}} |A|$. This improves recent results of Hanson and Roche-Newton.
DOI : 10.37236/7736
Classification : 52C10
Mots-clés : Cartesian products, few distinct distances

Cosmin Pohoata  1

1 California Institute of Technology 
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Cosmin Pohoata. On Cartesian products which determine few distinct distances. The electronic journal of combinatorics, Tome 26 (2019) no. 1. doi: 10.37236/7736

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