Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equilateral sets in the $\ell_1$ sum of Euclidean spaces   Let $E^n$ denote the (real) $n$-dimensional Euclidean space. It is not known
whether an equilateral set in the $\ell_1$ sum of $E^a$ and $E^b$, denoted here
as $E^a \oplus_1 E^b$, has maximum size at least $\dim(E^a \oplus_1 E^b) + 1 =
a + b + 1$ for all pairs of $a$ and $b$. We show, via some explicit
constructions of equilateral sets, that this holds for all $a \leqslant 27$, as
well as some other instances.

11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc