Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower bound on the size of a quasirandom forcing set of permutations   A set $S$ of permutations is forcing if for any sequence $\{\Pi_i\}_{i \in
\mathbb{N}}$ of permutations where the density $d(\pi,\Pi_i)$ converges to
$\frac{1}{|\pi|!}$ for every permutation $\pi \in S$, it holds that
$\{\Pi_i\}_{i \in \mathbb{N}}$ is quasirandom. Graham asked whether there
exists an integer $k$ such that the set of all permutations of order $k$ is
forcing; this has been shown to be true for any $k\ge 4$. In particular, the
set of all twenty-four permutations of order $4$ is forcing. We provide the
first non-trivial lower bound on the size of a forcing set of permutations:
every forcing set of permutations (with arbitrary orders) contains at least
four permutations.

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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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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: patt-sol