Equilateral Sets in $${\mathcal{l}}_{p}^{d}$$

Clifford Smyth ()
Additional contact information
Clifford Smyth: University of North Carolina Greensboro, Department of Mathematics and Statistics

A chapter in Thirty Essays on Geometric Graph Theory, 2013, pp 483-487 from Springer

Abstract: Abstract If X is a Minkowski space, i.e., a finite-dimensional real normed space, then $$S \subset X$$ is an equilateral set if all pairs of points of S determine the same distance with respect to the norm. Kusner conjectured that $$e({\mathcal{l}}_{p}^{d}) = d + 1$$ for $$1 0 such that $$e({\mathcal{l}}_{p}^{d}) \leq {C}_{p}{d}^{1+2/(p-1)}$$ .

Keywords: Equilateral Sets; Finite Dimensional Real Normed Space; Minkowski Space; Banach Mazur Compactum; Swanepoel (search for similar items in EconPapers)
Date: 2013
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-0110-0_25

Ordering information: This item can be ordered from
http://www.springer.com/9781461401100

DOI: 10.1007/978-1-4614-0110-0_25

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().