Homotheties and incidences

Dror Aiger; Micha Sharir

doi:10.1016/j.disc.2018.04.003

Homotheties and incidences

Dror Aiger, Micha Sharir

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

1 Scopus citations

Abstract

We consider problems involving rich homotheties in a set S of n points in the plane (that is, homotheties that map many points of S to other points of S). By reducing these problems to incidence problems involving points and lines in R³, we are able to obtain refined and new bounds for the number of rich homotheties, and for the number of distinct equivalence classes, under homotheties, of k-element subsets of S, for any k≥3. We also discuss the extensions of these problems to three and higher dimensions.

Original language	English
Pages (from-to)	2011-2017
Number of pages	7
Journal	Discrete Mathematics
Volume	341
Issue number	7
DOIs	https://doi.org/10.1016/j.disc.2018.04.003
State	Published - 1 Jul 2018
Externally published	Yes

Keywords

Combinatorial geometry
Homothety transformation
Incidences

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2018.04.003

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AB - We consider problems involving rich homotheties in a set S of n points in the plane (that is, homotheties that map many points of S to other points of S). By reducing these problems to incidence problems involving points and lines in R3, we are able to obtain refined and new bounds for the number of rich homotheties, and for the number of distinct equivalence classes, under homotheties, of k-element subsets of S, for any k≥3. We also discuss the extensions of these problems to three and higher dimensions.

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KW - Homothety transformation

KW - Incidences

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Homotheties and incidences

Abstract

Keywords

ASJC Scopus subject areas

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