A Lower Bound for the Translative Kissing Numbers of Simplices

Talata, István

doi:10.1007/s004930070026

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2018

2023

Publication Types

Select...

Article2

Book1

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Combinatorial Distance Geometry in Normed Spaces

Swanepoel

2018

Bolyai Society Mathematical Studies

View full text Add to dashboard Cite

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.

show abstract