Equilateral sets in the ℓ1 sum of Euclidean spaces

Lin, Aaron (2020) Equilateral sets in the ℓ1 sum of Euclidean spaces Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 61 (1). pp. 151-155. ISSN 0138-4821

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Let En denote the (real) n-dimensional Euclidean space. It is not known whether an equilateral set in the ℓ1 sum of Ea and Eb , denoted here as Ea⊕1Eb , has maximum size at least dim(Ea⊕1Eb)+1=a+b+1 for all pairs of a and b. We show, via some explicit constructions of equilateral sets, that this holds for all a⩽27 , as well as some other instances.

Item Type	Article
Keywords	equilateral sets,normed spaces,regular simplices
Departments	Mathematics
DOI	10.1007/s13366-019-00455-w
Date Deposited	07 Jun 2019 23:09
URI	https://researchonline.lse.ac.uk/id/eprint/100995