Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite two-distance tight frames   A finite collection of unit vectors $S \subset \mathbb{R}^n$ is called a
spherical two-distance set if there are two numbers $a$ and $b$ such that the
inner products of distinct vectors from $S$ are either $a$ or $b$. We prove
that if $a\ne -b,$ then a two-distance set that forms a tight frame for
$\mathbb{R}^n$ is a spherical embedding of a strongly regular graph, and every
strongly regular graph gives rise to two-distance tight frames through standard
spherical embeddings. Together with an earlier work by S. Waldron on the
equiangular case ({\em Linear Alg. Appl.}, vol. 41, pp. 2228-2242, 2009) this
completely characterizes two-distance tight frames. As an intermediate result,
we obtain a classification of all two-distance 2-designs.\

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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio