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

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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",

note = "Publisher Copyright: {\textcopyright} 2017, J{\'a}nos Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature.",

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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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UR - https://www.scopus.com/pages/publications/85012154474#tab=citedBy

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DO - 10.1007/s00493-016-3665-6

M3 - Article

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EP - 1100

JO - Combinatorica

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ER -

The Additive Structure of Cartesian Products Spanning Few Distinct Distances

Abstract

All Science Journal Classification (ASJC) codes

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