Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The tropical Cayley-Menger variety   The Cayley-Menger variety is the Zariski closure of the set of vectors
specifying the pairwise squared distances between $n$ points in $\mathbb{R}^d$.
This variety is fundamental to algebraic approaches in rigidity theory. We
study the tropicalization of the Cayley-Menger variety. In particular, when $d
= 2$, we show that it is the Minkowski sum of the set of ultrametrics on $n$
leaves with itself, and we describe its polyhedral structure. We then give a
new, tropical, proof of Laman's theorem.

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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin