Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universality of vector sequences and universality of Tverberg partitions   A result of Rosenthal says that for every $q>1$ and $n \in \mathbb{N}$ there
is $N \in \mathbb{N}$ such that every sequence of $N$ distinct positive numbers
contains, after a suitable translation and possible multiplication by $-1$, a
subsequence $a_1,\ldots,a_n$ that is either $q$-increasing (that is,
$a_{i+1}>qa_i$ for all $i$) or $1/q$-decreasing ($a_{i+1}<a_i/q$ for all $i$).
One of our main theorems extends this result to vector sequences. This theorem
is then used to prove the universality theorem for Tverberg partitions which
says that, for every $d$ and $r$, every long enough sequence of points in
$\mathbb{R}^d$ in general position contains a subsequence of length $n$ whose
Tverberg partitions are exactly the so called rainbow partitions.

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The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
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The categories of this paper are: eess
12
The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas