Equilateral sets in the ℓ1 sum of Euclidean spaces
Lin, A.
(2020).
Equilateral sets in the ℓ1 sum of Euclidean spaces.
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry,
61(1), 151-155.
https://doi.org/10.1007/s13366-019-00455-w
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.
