The Additive Structure of Cartesian Products Spanning Few Distinct Distances

Brandon Hanson

doi:10.1007/s00493-016-3665-6

The Additive Structure of Cartesian Products Spanning Few Distinct Distances

Brandon Hanson

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Guth and Katz proved that any point set P in the plane determines Ω(|P|/log |P|) distinct distances. We show that when near to this lower bound, a point set P of the form A × A must satisfy |A-A|≪|A-A|^2-1/8.

Original language	English (US)
Pages (from-to)	1095-1100
Number of pages	6
Journal	Combinatorica
Volume	38
Issue number	5
DOIs	https://doi.org/10.1007/s00493-016-3665-6
State	Published - Oct 1 2018

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Computational Mathematics

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10.1007/s00493-016-3665-6

Cite this

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title = "The Additive Structure of Cartesian Products Spanning Few Distinct Distances",

abstract = "Guth and Katz proved that any point set P in the plane determines Ω(|P|/log |P|) distinct distances. We show that when near to this lower bound, a point set P of the form A × A must satisfy |A-A|≪|A-A|2-1/8.",

author = "Brandon Hanson",

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AB - Guth and Katz proved that any point set P in the plane determines Ω(|P|/log |P|) distinct distances. We show that when near to this lower bound, a point set P of the form A × A must satisfy |A-A|≪|A-A|2-1/8.

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The Additive Structure of Cartesian Products Spanning Few Distinct Distances

Abstract

All Science Journal Classification (ASJC) codes

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