Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariable generation of the symmetric group   We say that permutations $\pi_1,\dots, \pi_r \in \mathcal{S}_n$ invariably
generate $\mathcal{S}_n$ if, no matter how one chooses conjugates
$\pi'_1,\dots,\pi'_r$ of these permutations, $\pi'_1,\dots,\pi'_r$ generate
$\mathcal{S}_n$. We show that if $\pi_1,\pi_2,\pi_3$ are chosen randomly from
$\mathcal{S}_n$ then, with probability tending to 1 as $n \rightarrow \infty$,
they do not invariably generate $\mathcal{S}_n$. By contrast it was shown
recently by Pemantle, Peres and Rivin that four random elements do invariably
generate $\mathcal{S}_n$ with positive probability. We include a proof of this
statement which, while sharing many features with their argument, is short and
completely combinatorial.

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The categories of this paper are: bayes-an
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
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The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int