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Combinatorial distance geometry in normed spaces

Swanepoel, Konrad ORCID: 0000-0002-1668-887X (2018) Combinatorial distance geometry in normed spaces. In: Ambrus, Gergely, Barany, Imre, Boroczky, Karoly J., Fejes Toth, Gabor and Pach, János, (eds.) New Trends in Intuitive Geometry. Bolyai Society Mathematical Studies. Springer-Verlag, Berlin, Germany, 407 - 458. ISBN 9783662574126

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Identification Number: 10.1007/978-3-662-57413-3_17

Abstract

We survey problems and results from combinatorial geometry in normed spaces, concentrating on problems that involve distances. These include various properties of unit-distance graphs, minimum-distance graphs, diameter graphs, as well as minimum spanning trees and Steiner minimum trees. In particular, we discuss translative kissing (or Hadwiger) numbers, equilateral sets, and the Borsuk problem in normed spaces. We show how to use the angular measure of Peter Brass to prove various statements about Hadwiger and blocking numbers of convex bodies in the plane, including some new results. We also include some new results on thin cones and their application to distinct distances and other combinatorial problems for normed spaces.

Item Type: Book Section
Official URL: https://www.springer.com/gp/book/9783662574126
Additional Information: © 2018 Springer
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 08 May 2017 15:46
Last Modified: 12 Jul 2020 18:03
URI: http://eprints.lse.ac.uk/id/eprint/76025

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